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Devshruti Pahuja

2004-Jun-11 09:26 UTC

[R] Regression query

Hi

I have a set of data with both quantitative and categorical predictors.
After scaling of response variable, i looked for multicollinearity (VIF
values)
among the predictors and removed the predictors who were hinding some of the
other significant
predictors. I'm curious to know whether the predictors (who are not
significant)
while doing simple 'lm' will be involved in interactions. How do i take
into
account
interactions of those predictors whom i removed just on the basis of
multicollinearity ?

I'll appreciate if someone can throw some light on this matter and how to
use R to detect
the interactions effectively .

Thanks

Regards
Dev

------Final 'lm model'--------------------> logmodelfull_minus_run_hr_walk_batting <- lm(log(salary) ~ hit+rbi +
walk+ obp +
strike.out+free.agent.eligible+free.agent.1991+arbitr.elgible.)> summary(logmodelfull_minus_run_hr_walk_batting)
Call:
lm(formula = log(salary) ~ hit + rbi + walk + obp + strike.out +
    free.agent.eligible + free.agent.1991 + arbitr.elgible.)

Residuals:
     Min       1Q   Median       3Q      Max
-2.41786 -0.28911 -0.02814  0.31890  1.49007

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)
(Intercept)           5.340782   0.251218  21.260  < 2e-16 ***
hit                   0.004479   0.001158   3.867 0.000133 ***
rbi                   0.011102   0.002195   5.059 7.05e-07 ***
walk                  0.005421   0.002206   2.457 0.014533 *
obp                  -1.385584   0.824105  -1.681 0.093653 .
strike.out           -0.005399   0.001438  -3.755 0.000205 ***
free.agent.eligible1  1.611521   0.080657  19.980  < 2e-16 ***
free.agent.19911     -0.301243   0.103481  -2.911 0.003848 **
arbitr.elgible.1      1.293059   0.086696  14.915  < 2e-16 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` '
1

Residual standard error: 0.5351 on 328 degrees of freedom
Multiple R-Squared: 0.7981,     Adjusted R-squared: 0.7932
F-statistic: 162.1 on 8 and 328 DF,  p-value: < 2.2e-16

----------------------------------------------------------------------------
----------------------------------------------------


--------------with
interactions----------------------------------------------------------------
---------------------------
>
> summary(baseball.lgmodel_with_interactions_ALL_arbid)
Call:
lm(formula = log(salary) ~ hit + rbi + strike.out + free.agent.eligible +
    free.agent.1991 + arbitr.elgible. + hit * free.agent.1991 +
    hit * arbitr.elgible. + hit * rbi + rbi * free.agent.eligible +
    rbi * arbitr.elgible. + rbi * arbitr.1991 + hit * strike.out +
    strike.out * free.agent.eligible + strike.out * arbitr.elgible. +
    strike.out * run + strike.out * hr + hit * free.agent.eligible +
    free.agent.eligible * run + hit * free.agent.1991 + strike.out *
    free.agent.1991 + free.agent.1991 * batting + free.agent.1991 *
    obp + arbitr.elgible. * run + batting * double + obp * run +
    obp * hr + walk * stolen.base + hit * arbitr.1991 + free.agent.eligible
*
    double + arbitr.elgible. * double + strike.out * triple +
    triple * batting + triple * walk + triple * walk + hit *
    hr + rbi * hr + free.agent.eligible * hr + free.agent.1991 *
    hr + arbitr.elgible. * hr + hr * arbitr.1991 + hit * walk +
    free.agent.eligible * walk + walk * rbi + rbi * stolen.base +
    strike.out * stolen.base + stolen.base * batting + stolen.base *
    walk + stolen.base * rbi + stolen.base * walk + arbitr.elgible. *
    error)

Residuals:
     Min       1Q   Median       3Q      Max
-2.29352 -0.28287 -0.03748  0.29790  1.31590

Coefficients:
                                  Estimate Std. Error t value Pr(>|t|)
(Intercept)                      5.217e+00  3.467e-01  15.048  < 2e-16 ***
hit                              6.927e-03  6.226e-03   1.112 0.266889
rbi                              1.908e-02  1.150e-02   1.658 0.098350 .
strike.out                      -5.692e-03  4.586e-03  -1.241 0.215517
free.agent.eligible1             1.287e+00  2.259e-01   5.699 3.05e-08 ***
free.agent.19911                 3.828e-01  6.575e-01   0.582 0.560914
arbitr.elgible.1                 1.038e+00  2.195e-01   4.726 3.63e-06 ***
arbitr.19911                    -1.024e+00  4.392e-01  -2.331 0.020443 *
run                              4.932e-02  2.905e-02   1.698 0.090682 .
hr                              -1.093e-01  7.208e-02  -1.516 0.130543
batting                         -1.814e-01  2.558e+00  -0.071 0.943522
obp                             -1.375e+00  2.253e+00  -0.610 0.542099
double                          -5.259e-02  4.489e-02  -1.172 0.242349
walk                             1.395e-02  9.757e-03   1.430 0.153808
stolen.base                     -1.685e-02  4.299e-02  -0.392 0.695372
triple                          -1.367e-01  1.600e-01  -0.854 0.393807
error                           -4.097e-03  6.879e-03  -0.595 0.552007
hit:free.agent.19911             8.248e-04  4.611e-03   0.179 0.858174
hit:arbitr.elgible.1             4.873e-03  6.448e-03   0.756 0.450395
hit:rbi                         -1.382e-04  7.709e-05  -1.792 0.074184 .
rbi:free.agent.eligible1         5.352e-03  9.555e-03   0.560 0.575855
rbi:arbitr.elgible.1            -3.384e-03  1.136e-02  -0.298 0.766072
rbi:arbitr.19911                 3.596e-02  2.179e-02   1.650 0.100046
hit:strike.out                   5.480e-06  5.446e-05   0.101 0.919917
strike.out:free.agent.eligible1 -2.570e-03  4.282e-03  -0.600 0.548890
strike.out:arbitr.elgible.1     -9.703e-04  5.234e-03  -0.185 0.853068
strike.out:run                   1.685e-04  1.246e-04   1.352 0.177345
strike.out:hr                   -3.088e-04  2.277e-04  -1.356 0.176229
hit:free.agent.eligible1        -1.359e-03  6.224e-03  -0.218 0.827363
free.agent.eligible1:run         1.248e-02  9.109e-03   1.370 0.171917
strike.out:free.agent.19911     -1.851e-02  5.974e-03  -3.099 0.002140 **
free.agent.19911:batting         7.076e-01  6.200e+00   0.114 0.909215
free.agent.19911:obp            -1.421e+00  3.952e+00  -0.360 0.719394
arbitr.elgible.1:run            -8.541e-03  8.773e-03  -0.974 0.331100
batting:double                   2.346e-01  1.609e-01   1.458 0.145884
run:obp                         -1.825e-01  7.492e-02  -2.436 0.015462 *
hr:obp                           3.687e-01  2.116e-01   1.742 0.082608 .
walk:stolen.base                -6.789e-05  1.557e-04  -0.436 0.663083
hit:arbitr.19911                -5.835e-03  7.084e-03  -0.824 0.410808
free.agent.eligible1:double     -1.151e-02  1.663e-02  -0.692 0.489334
arbitr.elgible.1:double          2.169e-03  1.938e-02   0.112 0.910985
strike.out:triple               -8.106e-04  6.023e-04  -1.346 0.179475
batting:triple                   5.179e-01  5.599e-01   0.925 0.355841
walk:triple                      8.755e-04  9.262e-04   0.945 0.345349
hit:hr                          -3.320e-04  2.626e-04  -1.264 0.207180
rbi:hr                           4.748e-04  3.015e-04   1.575 0.116414
free.agent.eligible1:hr          1.840e-02  2.313e-02   0.796 0.426972
free.agent.19911:hr              7.216e-02  1.889e-02   3.819 0.000165 ***
arbitr.elgible.1:hr              4.111e-02  2.803e-02   1.467 0.143564
arbitr.19911:hr                 -2.368e-02  4.647e-02  -0.510 0.610723
hit:walk                         3.173e-05  7.826e-05   0.405 0.685442
free.agent.eligible1:walk       -5.423e-03  4.984e-03  -1.088 0.277472
rbi:walk                        -7.569e-05  1.313e-04  -0.577 0.564598
rbi:stolen.base                  3.980e-05  1.605e-04   0.248 0.804409
strike.out:stolen.base          -2.611e-04  1.615e-04  -1.617 0.107004
batting:stolen.base              1.552e-01  1.434e-01   1.082 0.280020
arbitr.elgible.1:error           3.930e-03  1.390e-02   0.283 0.777495
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` '
1

Residual standard error: 0.4925 on 280 degrees of freedom
Multiple R-Squared: 0.854,      Adjusted R-squared: 0.8248
F-statistic: 29.24 on 56 and 280 DF,  p-value: < 2.2e-16

Devshruti Pahuja

2004-Jun-11 09:35 UTC

head link

[R] Regression query

Hi

I have a set of data with both quantitative and categorical predictors.
After scaling of response variable, i looked for multicollinearity (VIF
values) among the predictors and removed the predictors who were hinding
some of the
other significant predictors. I'm curious to know whether the predictors
(who are not significant) while doing simple 'lm' will be involved in
interactions. How do i take into
account  interactions of those predictors whom i removed just on the basis
of  multicollinearity ?

 I'll appreciate if someone can throw some light on this matter and how to
use R to detect the interactions effectively .

Thanks

 Regards
 Dev
> ------Final 'lm model'--------------------
> > logmodelfull_minus_run_hr_walk_batting <- lm(log(salary) ~ hit+rbi
+
walk> + obp + strike.out+free.agent.eligible+free.agent.1991+arbitr.elgible.)
> > summary(logmodelfull_minus_run_hr_walk_batting)
>
> Call:
> lm(formula = log(salary) ~ hit + rbi + walk + obp + strike.out +
>     free.agent.eligible + free.agent.1991 + arbitr.elgible.)
>
> Residuals:
>      Min       1Q   Median       3Q      Max
> -2.41786 -0.28911 -0.02814  0.31890  1.49007
>
> Coefficients:
>                       Estimate Std. Error t value Pr(>|t|)
> (Intercept)           5.340782   0.251218  21.260  < 2e-16 ***
> hit                   0.004479   0.001158   3.867 0.000133 ***
> rbi                   0.011102   0.002195   5.059 7.05e-07 ***
> walk                  0.005421   0.002206   2.457 0.014533 *
> obp                  -1.385584   0.824105  -1.681 0.093653 .
> strike.out           -0.005399   0.001438  -3.755 0.000205 ***
> free.agent.eligible1  1.611521   0.080657  19.980  < 2e-16 ***
> free.agent.19911     -0.301243   0.103481  -2.911 0.003848 **
> arbitr.elgible.1      1.293059   0.086696  14.915  < 2e-16 ***
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 `
' 1
>
> Residual standard error: 0.5351 on 328 degrees of freedom
> Multiple R-Squared: 0.7981,     Adjusted R-squared: 0.7932
> F-statistic: 162.1 on 8 and 328 DF,  p-value: < 2.2e-16
>
> --------------------------------------------------------------------------
--> ----------------------------------------------------
>
>
> --------------with
>
interactions----------------------------------------------------------------> ---------------------------
>
> >
> > summary(baseball.lgmodel_with_interactions_ALL_arbid)
>
> Call:
> lm(formula = log(salary) ~ hit + rbi + strike.out + free.agent.eligible +
>     free.agent.1991 + arbitr.elgible. + hit * free.agent.1991 +
>     hit * arbitr.elgible. + hit * rbi + rbi * free.agent.eligible +
>     rbi * arbitr.elgible. + rbi * arbitr.1991 + hit * strike.out +
>     strike.out * free.agent.eligible + strike.out * arbitr.elgible. +
>     strike.out * run + strike.out * hr + hit * free.agent.eligible +
>     free.agent.eligible * run + hit * free.agent.1991 + strike.out *
>     free.agent.1991 + free.agent.1991 * batting + free.agent.1991 *
>     obp + arbitr.elgible. * run + batting * double + obp * run +
>     obp * hr + walk * stolen.base + hit * arbitr.1991 +
free.agent.eligible> *
>     double + arbitr.elgible. * double + strike.out * triple +
>     triple * batting + triple * walk + triple * walk + hit *
>     hr + rbi * hr + free.agent.eligible * hr + free.agent.1991 *
>     hr + arbitr.elgible. * hr + hr * arbitr.1991 + hit * walk +
>     free.agent.eligible * walk + walk * rbi + rbi * stolen.base +
>     strike.out * stolen.base + stolen.base * batting + stolen.base *
>     walk + stolen.base * rbi + stolen.base * walk + arbitr.elgible. *
>     error)
>
> Residuals:
>      Min       1Q   Median       3Q      Max
> -2.29352 -0.28287 -0.03748  0.29790  1.31590
>
> Coefficients:
>                                   Estimate Std. Error t value Pr(>|t|)
> (Intercept)                      5.217e+00  3.467e-01  15.048  < 2e-16
***
> hit                              6.927e-03  6.226e-03   1.112 0.266889
> rbi                              1.908e-02  1.150e-02   1.658 0.098350 .
> strike.out                      -5.692e-03  4.586e-03  -1.241 0.215517
> free.agent.eligible1             1.287e+00  2.259e-01   5.699 3.05e-08 ***
> free.agent.19911                 3.828e-01  6.575e-01   0.582 0.560914
> arbitr.elgible.1                 1.038e+00  2.195e-01   4.726 3.63e-06 ***
> arbitr.19911                    -1.024e+00  4.392e-01  -2.331 0.020443 *
> run                              4.932e-02  2.905e-02   1.698 0.090682 .
> hr                              -1.093e-01  7.208e-02  -1.516 0.130543
> batting                         -1.814e-01  2.558e+00  -0.071 0.943522
> obp                             -1.375e+00  2.253e+00  -0.610 0.542099
> double                          -5.259e-02  4.489e-02  -1.172 0.242349
> walk                             1.395e-02  9.757e-03   1.430 0.153808
> stolen.base                     -1.685e-02  4.299e-02  -0.392 0.695372
> triple                          -1.367e-01  1.600e-01  -0.854 0.393807
> error                           -4.097e-03  6.879e-03  -0.595 0.552007
> hit:free.agent.19911             8.248e-04  4.611e-03   0.179 0.858174
> hit:arbitr.elgible.1             4.873e-03  6.448e-03   0.756 0.450395
> hit:rbi                         -1.382e-04  7.709e-05  -1.792 0.074184 .
> rbi:free.agent.eligible1         5.352e-03  9.555e-03   0.560 0.575855
> rbi:arbitr.elgible.1            -3.384e-03  1.136e-02  -0.298 0.766072
> rbi:arbitr.19911                 3.596e-02  2.179e-02   1.650 0.100046
> hit:strike.out                   5.480e-06  5.446e-05   0.101 0.919917
> strike.out:free.agent.eligible1 -2.570e-03  4.282e-03  -0.600 0.548890
> strike.out:arbitr.elgible.1     -9.703e-04  5.234e-03  -0.185 0.853068
> strike.out:run                   1.685e-04  1.246e-04   1.352 0.177345
> strike.out:hr                   -3.088e-04  2.277e-04  -1.356 0.176229
> hit:free.agent.eligible1        -1.359e-03  6.224e-03  -0.218 0.827363
> free.agent.eligible1:run         1.248e-02  9.109e-03   1.370 0.171917
> strike.out:free.agent.19911     -1.851e-02  5.974e-03  -3.099 0.002140 **
> free.agent.19911:batting         7.076e-01  6.200e+00   0.114 0.909215
> free.agent.19911:obp            -1.421e+00  3.952e+00  -0.360 0.719394
> arbitr.elgible.1:run            -8.541e-03  8.773e-03  -0.974 0.331100
> batting:double                   2.346e-01  1.609e-01   1.458 0.145884
> run:obp                         -1.825e-01  7.492e-02  -2.436 0.015462 *
> hr:obp                           3.687e-01  2.116e-01   1.742 0.082608 .
> walk:stolen.base                -6.789e-05  1.557e-04  -0.436 0.663083
> hit:arbitr.19911                -5.835e-03  7.084e-03  -0.824 0.410808
> free.agent.eligible1:double     -1.151e-02  1.663e-02  -0.692 0.489334
> arbitr.elgible.1:double          2.169e-03  1.938e-02   0.112 0.910985
> strike.out:triple               -8.106e-04  6.023e-04  -1.346 0.179475
> batting:triple                   5.179e-01  5.599e-01   0.925 0.355841
> walk:triple                      8.755e-04  9.262e-04   0.945 0.345349
> hit:hr                          -3.320e-04  2.626e-04  -1.264 0.207180
> rbi:hr                           4.748e-04  3.015e-04   1.575 0.116414
> free.agent.eligible1:hr          1.840e-02  2.313e-02   0.796 0.426972
> free.agent.19911:hr              7.216e-02  1.889e-02   3.819 0.000165 ***
> arbitr.elgible.1:hr              4.111e-02  2.803e-02   1.467 0.143564
> arbitr.19911:hr                 -2.368e-02  4.647e-02  -0.510 0.610723
> hit:walk                         3.173e-05  7.826e-05   0.405 0.685442
> free.agent.eligible1:walk       -5.423e-03  4.984e-03  -1.088 0.277472
> rbi:walk                        -7.569e-05  1.313e-04  -0.577 0.564598
> rbi:stolen.base                  3.980e-05  1.605e-04   0.248 0.804409
> strike.out:stolen.base          -2.611e-04  1.615e-04  -1.617 0.107004
> batting:stolen.base              1.552e-01  1.434e-01   1.082 0.280020
> arbitr.elgible.1:error           3.930e-03  1.390e-02   0.283 0.777495
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 `
' 1
>
> Residual standard error: 0.4925 on 280 degrees of freedom
> Multiple R-Squared: 0.854,      Adjusted R-squared: 0.8248
> F-statistic: 29.24 on 56 and 280 DF,  p-value: < 2.2e-16
>

Devshruti Pahuja

2004-Jun-11 10:08 UTC

head link

[R] Regression query

Hi

I have a set of data with both quantitative and categorical predictors.
After scaling of response variable, i looked for multicollinearity (VIF
values) among the predictors and removed the predictors who were hinding
some of the
other significant predictors. I'm curious to know whether the predictors
(who are not significant) while doing simple 'lm' will be involved in
interactions. How do i take into
account  interactions of those predictors whom i removed just on the basis
of  multicollinearity ?

 I'll appreciate if someone can throw some light on this matter and how to
use R to detect the interactions effectively .

Thanks

 Regards
 Dev
> ------Final 'lm model'--------------------
> > logmodelfull_minus_run_hr_walk_batting <- lm(log(salary) ~ hit+rbi
+
walk> + obp + strike.out+free.agent.eligible+free.agent.1991+arbitr.elgible.)
> > summary(logmodelfull_minus_run_hr_walk_batting)
>
> Call:
> lm(formula = log(salary) ~ hit + rbi + walk + obp + strike.out +
>     free.agent.eligible + free.agent.1991 + arbitr.elgible.)
>
> Residuals:
>      Min       1Q   Median       3Q      Max
> -2.41786 -0.28911 -0.02814  0.31890  1.49007
>
> Coefficients:
>                       Estimate Std. Error t value Pr(>|t|)
> (Intercept)           5.340782   0.251218  21.260  < 2e-16 ***
> hit                   0.004479   0.001158   3.867 0.000133 ***
> rbi                   0.011102   0.002195   5.059 7.05e-07 ***
> walk                  0.005421   0.002206   2.457 0.014533 *
> obp                  -1.385584   0.824105  -1.681 0.093653 .
> strike.out           -0.005399   0.001438  -3.755 0.000205 ***
> free.agent.eligible1  1.611521   0.080657  19.980  < 2e-16 ***
> free.agent.19911     -0.301243   0.103481  -2.911 0.003848 **
> arbitr.elgible.1      1.293059   0.086696  14.915  < 2e-16 ***
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 `
' 1
>
> Residual standard error: 0.5351 on 328 degrees of freedom
> Multiple R-Squared: 0.7981,     Adjusted R-squared: 0.7932
> F-statistic: 162.1 on 8 and 328 DF,  p-value: < 2.2e-16
>
> --------------------------------------------------------------------------
--> ----------------------------------------------------
>
>
> --------------with
>
interactions----------------------------------------------------------------> ---------------------------
>
> >
> > summary(baseball.lgmodel_with_interactions_ALL_arbid)
>
> Call:
> lm(formula = log(salary) ~ hit + rbi + strike.out + free.agent.eligible +
>     free.agent.1991 + arbitr.elgible. + hit * free.agent.1991 +
>     hit * arbitr.elgible. + hit * rbi + rbi * free.agent.eligible +
>     rbi * arbitr.elgible. + rbi * arbitr.1991 + hit * strike.out +
>     strike.out * free.agent.eligible + strike.out * arbitr.elgible. +
>     strike.out * run + strike.out * hr + hit * free.agent.eligible +
>     free.agent.eligible * run + hit * free.agent.1991 + strike.out *
>     free.agent.1991 + free.agent.1991 * batting + free.agent.1991 *
>     obp + arbitr.elgible. * run + batting * double + obp * run +
>     obp * hr + walk * stolen.base + hit * arbitr.1991 +
free.agent.eligible> *
>     double + arbitr.elgible. * double + strike.out * triple +
>     triple * batting + triple * walk + triple * walk + hit *
>     hr + rbi * hr + free.agent.eligible * hr + free.agent.1991 *
>     hr + arbitr.elgible. * hr + hr * arbitr.1991 + hit * walk +
>     free.agent.eligible * walk + walk * rbi + rbi * stolen.base +
>     strike.out * stolen.base + stolen.base * batting + stolen.base *
>     walk + stolen.base * rbi + stolen.base * walk + arbitr.elgible. *
>     error)
>
> Residuals:
>      Min       1Q   Median       3Q      Max
> -2.29352 -0.28287 -0.03748  0.29790  1.31590
>
> Coefficients:
>                                   Estimate Std. Error t value Pr(>|t|)
> (Intercept)                      5.217e+00  3.467e-01  15.048  < 2e-16
***
> hit                              6.927e-03  6.226e-03   1.112 0.266889
> rbi                              1.908e-02  1.150e-02   1.658 0.098350 
> strike.out                      -5.692e-03  4.586e-03  -1.241 0.215517
> free.agent.eligible1             1.287e+00  2.259e-01   5.699 3.05e-08 ***
> free.agent.19911                 3.828e-01  6.575e-01   0.582 0.560914
> arbitr.elgible.1                 1.038e+00  2.195e-01   4.726 3.63e-06 ***
> arbitr.19911                    -1.024e+00  4.392e-01  -2.331 0.020443 *
> run                              4.932e-02  2.905e-02   1.698 0.090682 
> hr                              -1.093e-01  7.208e-02  -1.516 0.130543
> batting                         -1.814e-01  2.558e+00  -0.071 0.943522
> obp                             -1.375e+00  2.253e+00  -0.610 0.542099
> double                          -5.259e-02  4.489e-02  -1.172 0.242349
> walk                             1.395e-02  9.757e-03   1.430 0.153808
> stolen.base                     -1.685e-02  4.299e-02  -0.392 0.695372
> triple                          -1.367e-01  1.600e-01  -0.854 0.393807
> error                           -4.097e-03  6.879e-03  -0.595 0.552007
> hit:free.agent.19911             8.248e-04  4.611e-03   0.179 0.858174
> hit:arbitr.elgible.1             4.873e-03  6.448e-03   0.756 0.450395
> hit:rbi                         -1.382e-04  7.709e-05  -1.792 0.074184 
> rbi:free.agent.eligible1         5.352e-03  9.555e-03   0.560 0.575855
> rbi:arbitr.elgible.1            -3.384e-03  1.136e-02  -0.298 0.766072
> rbi:arbitr.19911                 3.596e-02  2.179e-02   1.650 0.100046
> hit:strike.out                   5.480e-06  5.446e-05   0.101 0.919917
> strike.out:free.agent.eligible1 -2.570e-03  4.282e-03  -0.600 0.548890
> strike.out:arbitr.elgible.1     -9.703e-04  5.234e-03  -0.185 0.853068
> strike.out:run                   1.685e-04  1.246e-04   1.352 0.177345
> strike.out:hr                   -3.088e-04  2.277e-04  -1.356 0.176229
> hit:free.agent.eligible1        -1.359e-03  6.224e-03  -0.218 0.827363
> free.agent.eligible1:run         1.248e-02  9.109e-03   1.370 0.171917
> strike.out:free.agent.19911     -1.851e-02  5.974e-03  -3.099 0.002140 **
> free.agent.19911:batting         7.076e-01  6.200e+00   0.114 0.909215
> free.agent.19911:obp            -1.421e+00  3.952e+00  -0.360 0.719394
> arbitr.elgible.1:run            -8.541e-03  8.773e-03  -0.974 0.331100
> batting:double                   2.346e-01  1.609e-01   1.458 0.145884
> run:obp                         -1.825e-01  7.492e-02  -2.436 0.015462 *
> hr:obp                           3.687e-01  2.116e-01   1.742 0.082608 
> walk:stolen.base                -6.789e-05  1.557e-04  -0.436 0.663083
> hit:arbitr.19911                -5.835e-03  7.084e-03  -0.824 0.410808
> free.agent.eligible1:double     -1.151e-02  1.663e-02  -0.692 0.489334
> arbitr.elgible.1:double          2.169e-03  1.938e-02   0.112 0.910985
> strike.out:triple               -8.106e-04  6.023e-04  -1.346 0.179475
> batting:triple                   5.179e-01  5.599e-01   0.925 0.355841
> walk:triple                      8.755e-04  9.262e-04   0.945 0.345349
> hit:hr                          -3.320e-04  2.626e-04  -1.264 0.207180
> rbi:hr                           4.748e-04  3.015e-04   1.575 0.116414
> free.agent.eligible1:hr          1.840e-02  2.313e-02   0.796 0.426972
> free.agent.19911:hr              7.216e-02  1.889e-02   3.819 0.000165 ***
> arbitr.elgible.1:hr              4.111e-02  2.803e-02   1.467 0.143564
> arbitr.19911:hr                 -2.368e-02  4.647e-02  -0.510 0.610723
> hit:walk                         3.173e-05  7.826e-05   0.405 0.685442
> free.agent.eligible1:walk       -5.423e-03  4.984e-03  -1.088 0.277472
> rbi:walk                        -7.569e-05  1.313e-04  -0.577 0.564598
> rbi:stolen.base                  3.980e-05  1.605e-04   0.248 0.804409
> strike.out:stolen.base          -2.611e-04  1.615e-04  -1.617 0.107004
> batting:stolen.base              1.552e-01  1.434e-01   1.082 0.280020
> arbitr.elgible.1:error           3.930e-03  1.390e-02   0.283 0.777495
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 `
' 1
>
> Residual standard error: 0.4925 on 280 degrees of freedom
> Multiple R-Squared: 0.854,      Adjusted R-squared: 0.8248
> F-statistic: 29.24 on 56 and 280 DF,  p-value: < 2.2e-16
>
	[[alternative HTML version deleted]]

Peter Flom

2004-Jun-13 15:03 UTC

head link

[R] Regression query

If variables are colinear, then looking at interactions among them
doesn't make much sense.  High collinearity means that one variable is
nearly a linear combination of others.  IOW, that variable is not adding
much information.  So, if you look at the interaction, you are ALMOST
looking at a quadratic (e.g., if the collinearity involves only 2
variables, then one is very similar to the other, so X1*X2 is almost
X1*X1).  The output will be confusing, to say the least. 

Worse, when you include collinear variables, the resulting equation is
highly sensitive to small (sometimes very small) changes in the data. 
Belsley gives an example where changes in the third decimal place result
in totally different equations.

For details see Belsley's book titled something like "collinearity and
weak data in regression" (sorry, the book and my files are at the
office, but this should let you find it

HTH

Peter L. Flom, PhD
Assistant Director, Statistics and Data Analysis Core
Center for Drug Use and HIV Research
National Development and Research Institutes
71 W. 23rd St
www.peterflom.com
New York, NY 10010
(212) 845-4485 (voice)
(917) 438-0894 (fax)

>>> "Devshruti Pahuja" <devshruti at hotmail.com>
06/11/04 5:35 AM >>>Hi

I have a set of data with both quantitative and categorical predictors.
After scaling of response variable, i looked for multicollinearity (VIF
values) among the predictors and removed the predictors who were hinding
some of the
other significant predictors. I'm curious to know whether the predictors
(who are not significant) while doing simple 'lm' will be involved in
interactions. How do i take into
account  interactions of those predictors whom i removed just on the
basis
of  multicollinearity ?

 I'll appreciate if someone can throw some light on this matter and how
to
use R to detect the interactions effectively .

Thanks

 Regards
 Dev
> ------Final 'lm model'--------------------
> > logmodelfull_minus_run_hr_walk_batting <- lm(log(salary) ~ hit+rbi
+
walk> + obp +
strike.out+free.agent.eligible+free.agent.1991+arbitr.elgible.)> > summary(logmodelfull_minus_run_hr_walk_batting)
>
> Call:
> lm(formula = log(salary) ~ hit + rbi + walk + obp + strike.out +
>     free.agent.eligible + free.agent.1991 + arbitr.elgible.)
>
> Residuals:
>      Min       1Q   Median       3Q      Max
> -2.41786 -0.28911 -0.02814  0.31890  1.49007
>
> Coefficients:
>                       Estimate Std. Error t value Pr(>|t|)
> (Intercept)           5.340782   0.251218  21.260  < 2e-16 ***
> hit                   0.004479   0.001158   3.867 0.000133 ***
> rbi                   0.011102   0.002195   5.059 7.05e-07 ***
> walk                  0.005421   0.002206   2.457 0.014533 *
> obp                  -1.385584   0.824105  -1.681 0.093653 .
> strike.out           -0.005399   0.001438  -3.755 0.000205 ***
> free.agent.eligible1  1.611521   0.080657  19.980  < 2e-16 ***
> free.agent.19911     -0.301243   0.103481  -2.911 0.003848 **
> arbitr.elgible.1      1.293059   0.086696  14.915  < 2e-16 ***
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 `
' 1
>
> Residual standard error: 0.5351 on 328 degrees of freedom
> Multiple R-Squared: 0.7981,     Adjusted R-squared: 0.7932
> F-statistic: 162.1 on 8 and 328 DF,  p-value: < 2.2e-16
>
>--------------------------------------------------------------------------
--> ----------------------------------------------------
>
>
> --------------with
>
interactions----------------------------------------------------------------> ---------------------------
>
> >
> > summary(baseball.lgmodel_with_interactions_ALL_arbid)
>
> Call:
> lm(formula = log(salary) ~ hit + rbi + strike.out +
free.agent.eligible +>     free.agent.1991 + arbitr.elgible. + hit * free.agent.1991 +
>     hit * arbitr.elgible. + hit * rbi + rbi * free.agent.eligible +
>     rbi * arbitr.elgible. + rbi * arbitr.1991 + hit * strike.out +
>     strike.out * free.agent.eligible + strike.out * arbitr.elgible. +
>     strike.out * run + strike.out * hr + hit * free.agent.eligible +
>     free.agent.eligible * run + hit * free.agent.1991 + strike.out *
>     free.agent.1991 + free.agent.1991 * batting + free.agent.1991 *
>     obp + arbitr.elgible. * run + batting * double + obp * run +
>     obp * hr + walk * stolen.base + hit * arbitr.1991 +
free.agent.eligible> *
>     double + arbitr.elgible. * double + strike.out * triple +
>     triple * batting + triple * walk + triple * walk + hit *
>     hr + rbi * hr + free.agent.eligible * hr + free.agent.1991 *
>     hr + arbitr.elgible. * hr + hr * arbitr.1991 + hit * walk +
>     free.agent.eligible * walk + walk * rbi + rbi * stolen.base +
>     strike.out * stolen.base + stolen.base * batting + stolen.base *
>     walk + stolen.base * rbi + stolen.base * walk + arbitr.elgible. *
>     error)
>
> Residuals:
>      Min       1Q   Median       3Q      Max
> -2.29352 -0.28287 -0.03748  0.29790  1.31590
>
> Coefficients:
>                                   Estimate Std. Error t value Pr(>|t|)
> (Intercept)                      5.217e+00  3.467e-01  15.048  < 2e-16
***> hit                              6.927e-03  6.226e-03   1.112 0.266889
> rbi                              1.908e-02  1.150e-02   1.658 0.098350
.> strike.out                      -5.692e-03  4.586e-03  -1.241 0.215517
> free.agent.eligible1             1.287e+00  2.259e-01   5.699 3.05e-08
***> free.agent.19911                 3.828e-01  6.575e-01   0.582 0.560914
> arbitr.elgible.1                 1.038e+00  2.195e-01   4.726 3.63e-06
***> arbitr.19911                    -1.024e+00  4.392e-01  -2.331 0.020443
*> run                              4.932e-02  2.905e-02   1.698 0.090682
.> hr                              -1.093e-01  7.208e-02  -1.516 0.130543
> batting                         -1.814e-01  2.558e+00  -0.071 0.943522
> obp                             -1.375e+00  2.253e+00  -0.610 0.542099
> double                          -5.259e-02  4.489e-02  -1.172 0.242349
> walk                             1.395e-02  9.757e-03   1.430 0.153808
> stolen.base                     -1.685e-02  4.299e-02  -0.392 0.695372
> triple                          -1.367e-01  1.600e-01  -0.854 0.393807
> error                           -4.097e-03  6.879e-03  -0.595 0.552007
> hit:free.agent.19911             8.248e-04  4.611e-03   0.179 0.858174
> hit:arbitr.elgible.1             4.873e-03  6.448e-03   0.756 0.450395
> hit:rbi                         -1.382e-04  7.709e-05  -1.792 0.074184
.> rbi:free.agent.eligible1         5.352e-03  9.555e-03   0.560 0.575855
> rbi:arbitr.elgible.1            -3.384e-03  1.136e-02  -0.298 0.766072
> rbi:arbitr.19911                 3.596e-02  2.179e-02   1.650 0.100046
> hit:strike.out                   5.480e-06  5.446e-05   0.101 0.919917
> strike.out:free.agent.eligible1 -2.570e-03  4.282e-03  -0.600 0.548890
> strike.out:arbitr.elgible.1     -9.703e-04  5.234e-03  -0.185 0.853068
> strike.out:run                   1.685e-04  1.246e-04   1.352 0.177345
> strike.out:hr                   -3.088e-04  2.277e-04  -1.356 0.176229
> hit:free.agent.eligible1        -1.359e-03  6.224e-03  -0.218 0.827363
> free.agent.eligible1:run         1.248e-02  9.109e-03   1.370 0.171917
> strike.out:free.agent.19911     -1.851e-02  5.974e-03  -3.099 0.002140
**> free.agent.19911:batting         7.076e-01  6.200e+00   0.114 0.909215
> free.agent.19911:obp            -1.421e+00  3.952e+00  -0.360 0.719394
> arbitr.elgible.1:run            -8.541e-03  8.773e-03  -0.974 0.331100
> batting:double                   2.346e-01  1.609e-01   1.458 0.145884
> run:obp                         -1.825e-01  7.492e-02  -2.436 0.015462
*> hr:obp                           3.687e-01  2.116e-01   1.742 0.082608
.> walk:stolen.base                -6.789e-05  1.557e-04  -0.436 0.663083
> hit:arbitr.19911                -5.835e-03  7.084e-03  -0.824 0.410808
> free.agent.eligible1:double     -1.151e-02  1.663e-02  -0.692 0.489334
> arbitr.elgible.1:double          2.169e-03  1.938e-02   0.112 0.910985
> strike.out:triple               -8.106e-04  6.023e-04  -1.346 0.179475
> batting:triple                   5.179e-01  5.599e-01   0.925 0.355841
> walk:triple                      8.755e-04  9.262e-04   0.945 0.345349
> hit:hr                          -3.320e-04  2.626e-04  -1.264 0.207180
> rbi:hr                           4.748e-04  3.015e-04   1.575 0.116414
> free.agent.eligible1:hr          1.840e-02  2.313e-02   0.796 0.426972
> free.agent.19911:hr              7.216e-02  1.889e-02   3.819 0.000165
***> arbitr.elgible.1:hr              4.111e-02  2.803e-02   1.467 0.143564
> arbitr.19911:hr                 -2.368e-02  4.647e-02  -0.510 0.610723
> hit:walk                         3.173e-05  7.826e-05   0.405 0.685442
> free.agent.eligible1:walk       -5.423e-03  4.984e-03  -1.088 0.277472
> rbi:walk                        -7.569e-05  1.313e-04  -0.577 0.564598
> rbi:stolen.base                  3.980e-05  1.605e-04   0.248 0.804409
> strike.out:stolen.base          -2.611e-04  1.615e-04  -1.617 0.107004
> batting:stolen.base              1.552e-01  1.434e-01   1.082 0.280020
> arbitr.elgible.1:error           3.930e-03  1.390e-02   0.283 0.777495
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 `
' 1
>
> Residual standard error: 0.4925 on 280 degrees of freedom
> Multiple R-Squared: 0.854,      Adjusted R-squared: 0.8248
> F-statistic: 29.24 on 56 and 280 DF,  p-value: < 2.2e-16
>
______________________________________________
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Liaw, Andy

2004-Jun-13 19:44 UTC

head link

[R] Regression query

> From: Peter Flom
> 
> If variables are colinear, then looking at interactions among them
> doesn't make much sense.  High collinearity means that one variable is
> nearly a linear combination of others.  IOW, that variable is 
> not adding
> much information.  So, if you look at the interaction, you are ALMOST
> looking at a quadratic (e.g., if the collinearity involves only 2
> variables, then one is very similar to the other, so X1*X2 is almost
> X1*X1).  The output will be confusing, to say the least. 
> 
> Worse, when you include collinear variables, the resulting equation is
> highly sensitive to small (sometimes very small) changes in the data. 
> Belsley gives an example where changes in the third decimal 
> place result
> in totally different equations.
> 
> For details see Belsley's book titled something like "collinearity
and
> weak data in regression" (sorry, the book and my files are at the
> office, but this should let you find it
I guess you're referring to: "Conditioning Diagnostics: Collinearity
and
Weak Data in Regression" (Wiley, 1992, rather pricey...).

Hocking has a plot that shows the effect of collinearity in a paper from the
early '80s (the "picket fence").  The plot is used on the cover of
his
latest linear model book, also published by Wiley, now in 2nd edition.  

[An exercise for R newbies:  Try reproducing that plot in R, probably using
the Scaterplot3D package.]

Best,
Andy

 > HTH
> 
> Peter L. Flom, PhD
> Assistant Director, Statistics and Data Analysis Core
> Center for Drug Use and HIV Research
> National Development and Research Institutes
> 71 W. 23rd St
> www.peterflom.com
> New York, NY 10010
> (212) 845-4485 (voice)
> (917) 438-0894 (fax)
> 
> 
> >>> "Devshruti Pahuja" <devshruti at hotmail.com>
06/11/04 5:35 AM >>>
> Hi
> 
> I have a set of data with both quantitative and categorical 
> predictors.
> After scaling of response variable, i looked for 
> multicollinearity (VIF
> values) among the predictors and removed the predictors who 
> were hinding
> some of the
> other significant predictors. I'm curious to know whether the 
> predictors
> (who are not significant) while doing simple 'lm' will be involved
in
> interactions. How do i take into
> account  interactions of those predictors whom i removed just on the
> basis
> of  multicollinearity ?
> 
>  I'll appreciate if someone can throw some light on this 
> matter and how
> to
> use R to detect the interactions effectively .
> 
> Thanks
> 
>  Regards
>  Dev
> 
> > ------Final 'lm model'--------------------
> > > logmodelfull_minus_run_hr_walk_batting <- lm(log(salary) 
> ~ hit+rbi +
> walk
> > + obp +
> strike.out+free.agent.eligible+free.agent.1991+arbitr.elgible.)
> > > summary(logmodelfull_minus_run_hr_walk_batting)
> >
> > Call:
> > lm(formula = log(salary) ~ hit + rbi + walk + obp + strike.out +
> >     free.agent.eligible + free.agent.1991 + arbitr.elgible.)
> >
> > Residuals:
> >      Min       1Q   Median       3Q      Max
> > -2.41786 -0.28911 -0.02814  0.31890  1.49007
> >
> > Coefficients:
> >                       Estimate Std. Error t value Pr(>|t|)
> > (Intercept)           5.340782   0.251218  21.260  < 2e-16 ***
> > hit                   0.004479   0.001158   3.867 0.000133 ***
> > rbi                   0.011102   0.002195   5.059 7.05e-07 ***
> > walk                  0.005421   0.002206   2.457 0.014533 *
> > obp                  -1.385584   0.824105  -1.681 0.093653 .
> > strike.out           -0.005399   0.001438  -3.755 0.000205 ***
> > free.agent.eligible1  1.611521   0.080657  19.980  < 2e-16 ***
> > free.agent.19911     -0.301243   0.103481  -2.911 0.003848 **
> > arbitr.elgible.1      1.293059   0.086696  14.915  < 2e-16 ***
> > ---
> > Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.'
0.1 ` ' 1
> >
> > Residual standard error: 0.5351 on 328 degrees of freedom
> > Multiple R-Squared: 0.7981,     Adjusted R-squared: 0.7932
> > F-statistic: 162.1 on 8 and 328 DF,  p-value: < 2.2e-16
> >
> >
> --------------------------------------------------------------
> ------------
> --
> > ----------------------------------------------------
> >
> >
> > --------------with
> >
> interactions--------------------------------------------------
> --------------
> > ---------------------------
> >
> > >
> > > summary(baseball.lgmodel_with_interactions_ALL_arbid)
> >
> > Call:
> > lm(formula = log(salary) ~ hit + rbi + strike.out +
> free.agent.eligible +
> >     free.agent.1991 + arbitr.elgible. + hit * free.agent.1991 +
> >     hit * arbitr.elgible. + hit * rbi + rbi * free.agent.eligible +
> >     rbi * arbitr.elgible. + rbi * arbitr.1991 + hit * strike.out +
> >     strike.out * free.agent.eligible + strike.out * 
> arbitr.elgible. +
> >     strike.out * run + strike.out * hr + hit * free.agent.eligible +
> >     free.agent.eligible * run + hit * free.agent.1991 + strike.out *
> >     free.agent.1991 + free.agent.1991 * batting + free.agent.1991 *
> >     obp + arbitr.elgible. * run + batting * double + obp * run +
> >     obp * hr + walk * stolen.base + hit * arbitr.1991 +
> free.agent.eligible
> > *
> >     double + arbitr.elgible. * double + strike.out * triple +
> >     triple * batting + triple * walk + triple * walk + hit *
> >     hr + rbi * hr + free.agent.eligible * hr + free.agent.1991 *
> >     hr + arbitr.elgible. * hr + hr * arbitr.1991 + hit * walk +
> >     free.agent.eligible * walk + walk * rbi + rbi * stolen.base +
> >     strike.out * stolen.base + stolen.base * batting + stolen.base *
> >     walk + stolen.base * rbi + stolen.base * walk + 
> arbitr.elgible. *
> >     error)
> >
> > Residuals:
> >      Min       1Q   Median       3Q      Max
> > -2.29352 -0.28287 -0.03748  0.29790  1.31590
> >
> > Coefficients:
> >                                   Estimate Std. Error t 
> value Pr(>|t|)
> > (Intercept)                      5.217e+00  3.467e-01  
> 15.048  < 2e-16
> ***
> > hit                              6.927e-03  6.226e-03   
> 1.112 0.266889
> > rbi                              1.908e-02  1.150e-02   
> 1.658 0.098350
> .
> > strike.out                      -5.692e-03  4.586e-03  
> -1.241 0.215517
> > free.agent.eligible1             1.287e+00  2.259e-01   
> 5.699 3.05e-08
> ***
> > free.agent.19911                 3.828e-01  6.575e-01   
> 0.582 0.560914
> > arbitr.elgible.1                 1.038e+00  2.195e-01   
> 4.726 3.63e-06
> ***
> > arbitr.19911                    -1.024e+00  4.392e-01  
> -2.331 0.020443
> *
> > run                              4.932e-02  2.905e-02   
> 1.698 0.090682
> .
> > hr                              -1.093e-01  7.208e-02  
> -1.516 0.130543
> > batting                         -1.814e-01  2.558e+00  
> -0.071 0.943522
> > obp                             -1.375e+00  2.253e+00  
> -0.610 0.542099
> > double                          -5.259e-02  4.489e-02  
> -1.172 0.242349
> > walk                             1.395e-02  9.757e-03   
> 1.430 0.153808
> > stolen.base                     -1.685e-02  4.299e-02  
> -0.392 0.695372
> > triple                          -1.367e-01  1.600e-01  
> -0.854 0.393807
> > error                           -4.097e-03  6.879e-03  
> -0.595 0.552007
> > hit:free.agent.19911             8.248e-04  4.611e-03   
> 0.179 0.858174
> > hit:arbitr.elgible.1             4.873e-03  6.448e-03   
> 0.756 0.450395
> > hit:rbi                         -1.382e-04  7.709e-05  
> -1.792 0.074184
> .
> > rbi:free.agent.eligible1         5.352e-03  9.555e-03   
> 0.560 0.575855
> > rbi:arbitr.elgible.1            -3.384e-03  1.136e-02  
> -0.298 0.766072
> > rbi:arbitr.19911                 3.596e-02  2.179e-02   
> 1.650 0.100046
> > hit:strike.out                   5.480e-06  5.446e-05   
> 0.101 0.919917
> > strike.out:free.agent.eligible1 -2.570e-03  4.282e-03  
> -0.600 0.548890
> > strike.out:arbitr.elgible.1     -9.703e-04  5.234e-03  
> -0.185 0.853068
> > strike.out:run                   1.685e-04  1.246e-04   
> 1.352 0.177345
> > strike.out:hr                   -3.088e-04  2.277e-04  
> -1.356 0.176229
> > hit:free.agent.eligible1        -1.359e-03  6.224e-03  
> -0.218 0.827363
> > free.agent.eligible1:run         1.248e-02  9.109e-03   
> 1.370 0.171917
> > strike.out:free.agent.19911     -1.851e-02  5.974e-03  
> -3.099 0.002140
> **
> > free.agent.19911:batting         7.076e-01  6.200e+00   
> 0.114 0.909215
> > free.agent.19911:obp            -1.421e+00  3.952e+00  
> -0.360 0.719394
> > arbitr.elgible.1:run            -8.541e-03  8.773e-03  
> -0.974 0.331100
> > batting:double                   2.346e-01  1.609e-01   
> 1.458 0.145884
> > run:obp                         -1.825e-01  7.492e-02  
> -2.436 0.015462
> *
> > hr:obp                           3.687e-01  2.116e-01   
> 1.742 0.082608
> .
> > walk:stolen.base                -6.789e-05  1.557e-04  
> -0.436 0.663083
> > hit:arbitr.19911                -5.835e-03  7.084e-03  
> -0.824 0.410808
> > free.agent.eligible1:double     -1.151e-02  1.663e-02  
> -0.692 0.489334
> > arbitr.elgible.1:double          2.169e-03  1.938e-02   
> 0.112 0.910985
> > strike.out:triple               -8.106e-04  6.023e-04  
> -1.346 0.179475
> > batting:triple                   5.179e-01  5.599e-01   
> 0.925 0.355841
> > walk:triple                      8.755e-04  9.262e-04   
> 0.945 0.345349
> > hit:hr                          -3.320e-04  2.626e-04  
> -1.264 0.207180
> > rbi:hr                           4.748e-04  3.015e-04   
> 1.575 0.116414
> > free.agent.eligible1:hr          1.840e-02  2.313e-02   
> 0.796 0.426972
> > free.agent.19911:hr              7.216e-02  1.889e-02   
> 3.819 0.000165
> ***
> > arbitr.elgible.1:hr              4.111e-02  2.803e-02   
> 1.467 0.143564
> > arbitr.19911:hr                 -2.368e-02  4.647e-02  
> -0.510 0.610723
> > hit:walk                         3.173e-05  7.826e-05   
> 0.405 0.685442
> > free.agent.eligible1:walk       -5.423e-03  4.984e-03  
> -1.088 0.277472
> > rbi:walk                        -7.569e-05  1.313e-04  
> -0.577 0.564598
> > rbi:stolen.base                  3.980e-05  1.605e-04   
> 0.248 0.804409
> > strike.out:stolen.base          -2.611e-04  1.615e-04  
> -1.617 0.107004
> > batting:stolen.base              1.552e-01  1.434e-01   
> 1.082 0.280020
> > arbitr.elgible.1:error           3.930e-03  1.390e-02   
> 0.283 0.777495
> > ---
> > Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.'
0.1 ` ' 1
> >
> > Residual standard error: 0.4925 on 280 degrees of freedom
> > Multiple R-Squared: 0.854,      Adjusted R-squared: 0.8248
> > F-statistic: 29.24 on 56 and 280 DF,  p-value: < 2.2e-16
> >
> 
> ______________________________________________
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> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html
> 
>

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