Hello R community, I have a question regarding correlation and regression analysis. I have two variables, x and y. Both have a standard deviation of 1; thus, correlation and slope from the linear regression (which also must have an intercept of zero) are equal. I want to probe two particular questions: 1) Is the slope significantly different from zero? This should be easy with the lm function, as the p-value should reflect exactly that question. If I am wrong, lease correct me. 2) Is the slope significantly different from a non-zero value (e.g. 0.5)? How can I probe that hypothesis? Any ideas? I apologize if this question is too trivial and already answered somewhere, but I did not find it. Thank you for the help! Christian
Hi Christian, please give always reproducible code, so we can see what have done and give you the best answer. lm function, generally as in this example form lm man page ( ?lm)> trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69) >ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14) >reg=lm(trt~ctl) >summary(reg)Call: lm(formula = trt ~ ctl) Residuals: Min 1Q Median 3Q Max -1.09389 -0.33069 -0.15249 0.05128 1.45497 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 7.7957 2.1661 3.599 0.00699 ** ctl -0.6230 0.4279 -1.456 0.18351 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.7485 on 8 degrees of freedom Multiple R-squared: 0.2095, Adjusted R-squared: 0.1106 F-statistic: 2.12 on 1 and 8 DF, p-value: 0.1835 Returns you all the answer (almost) for the questions that you ask; the p-value of the intercept line, is the p-value from the test( t test) if the intercept is different form zero. the ctl line has also the same interpretation, regarding the value returned. Meaning no is not significantly different form zero. If you want to test if the estimates ( slopes or intercept) are different from a specific value as in your case different for 0.5 you can apply a test. Type on R ?t.test and you can find the all the information you need. Hope this helps Best Regards Anna Anna Freni Sterrantino Ph.D Student Department of Statistics University of Bologna, Italy via Belle Arti 41, 40124 BO. ________________________________ Da: Christian Arnold <chrarnold@web.de> A: r-help@r-project.org Inviato: Martedì 9 dicembre 2008, 21:54:23 Oggetto: [R] Significance of slopes Hello R community, I have a question regarding correlation and regression analysis. I have two variables, x and y. Both have a standard deviation of 1; thus, correlation and slope from the linear regression (which also must have an intercept of zero) are equal. I want to probe two particular questions: 1) Is the slope significantly different from zero? This should be easy with the lm function, as the p-value should reflect exactly that question. If I am wrong, lease correct me. 2) Is the slope significantly different from a non-zero value (e.g. 0.5)? How can I probe that hypothesis? Any ideas? I apologize if this question is too trivial and already answered somewhere, but I did not find it. [[elided Yahoo spam]] Christian ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]]
Hi Christian, please give always reproducible code, so we can see what have done and give you the best answer. lm function, generally as in this example form lm man page ( ?lm)> trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69) >ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14) >reg=lm(trt~ctl) >summary(reg)Call: lm(formula = trt ~ ctl) Residuals: Min 1Q Median 3Q Max -1.09389 -0.33069 -0.15249 0.05128 1.45497 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 7.7957 2.1661 3.599 0.00699 ** ctl -0.6230 0.4279 -1.456 0.18351 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.7485 on 8 degrees of freedom Multiple R-squared: 0.2095, Adjusted R-squared: 0.1106 F-statistic: 2.12 on 1 and 8 DF, p-value: 0.1835 Returns you all the answer (almost) for the questions that you ask; the p-value of the intercept line, is the p-value from the test( t test) if the intercept is different form zero. the ctl line has also the same interpretation, regarding the value returned. Meaning no is not significantly different form zero. If you want to test if the estimates ( slopes or intercept) are different from a specific value as in your case different for 0.5 you can apply a test. Type on R ?t.test and you can find the all the information you need. Hope this helps Best Regards Anna Anna Freni Sterrantino Ph.D Student Department of Statistics University of Bologna, Italy via Belle Arti 41, 40124 BO. ________________________________ Da: Christian Arnold <chrarnold@web.de> A: r-help@r-project.org Inviato: Martedì 9 dicembre 2008, 21:54:23 Oggetto: [R] Significance of slopes Hello R community, I have a question regarding correlation and regression analysis. I have two variables, x and y. Both have a standard deviation of 1; thus, correlation and slope from the linear regression (which also must have an intercept of zero) are equal. I want to probe two particular questions: 1) Is the slope significantly different from zero? This should be easy with the lm function, as the p-value should reflect exactly that question. If I am wrong, lease correct me. 2) Is the slope significantly different from a non-zero value (e.g. 0.5)? How can I probe that hypothesis? Any ideas? I apologize if this question is too trivial and already answered somewhere, but I did not find it. [[elided Yahoo spam]] Christian ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]]
Hi r-help-bounces at r-project.org napsal dne 09.12.2008 23:21:17:> Hi Christian, > please give always reproducible code, > so we can see what have done > and give you the best answer. > > lm function, generally > as in this example form lm man page ( ?lm) > > > > trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69) > >ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14) > >reg=lm(trt~ctl) > >summary(reg) > > Call: > lm(formula = trt ~ ctl) > > Residuals: > Min 1Q Median 3Q Max > -1.09389 -0.33069 -0.15249 0.05128 1.45497 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) 7.7957 2.1661 3.599 0.00699 ** > ctl -0.6230 0.4279 -1.456 0.18351 > --- > Signif. codes: 0 ???***??? 0.001 ???**??? 0.01 ???*??? 0.05 ???.??? 0.1??? ??? 1> > Residual standard error: 0.7485 on 8 degrees of freedom > Multiple R-squared: 0.2095, Adjusted R-squared: 0.1106 > F-statistic: 2.12 on 1 and 8 DF, p-value: 0.1835 > > > Returns you all the answer (almost) for the questions that you ask; > the p-value of the intercept line, is the p-value from the > test( t test) if the intercept is different form zero. > the ctl line has also the same interpretation, regarding the valuereturned.> Meaning no is not significantly different form zero. > > If you want to test if the estimates ( slopes or intercept) are > different from a specific value as in your case different for 0.5 > you can apply a test.Or use offset test for slope == -1 reg=lm(trt~ctl+offset(-1*ctl)) summary(reg) Call: lm(formula = trt ~ ctl + offset(-1 * ctl)) Residuals: Min 1Q Median 3Q Max -1.09389 -0.33069 -0.15249 0.05128 1.45497 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 7.7957 2.1661 3.599 0.00699 ** ctl 0.3770 0.4279 0.881 0.40391 --- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 Residual standard error: 0.7485 on 8 degrees of freedom Multiple R-squared: 0.2095, Adjusted R-squared: 0.1106 F-statistic: 2.12 on 1 and 8 DF, p-value: 0.1835 test for slope == 0.5 reg=lm(trt~ctl+offset(0.5*ctl)) Regards Petr> Type on R > ?t.test > and you can find the all the information you need. > > Hope this helps > > Best Regards > > Anna > > Anna Freni Sterrantino > Ph.D Student > Department of Statistics > University of Bologna, Italy > via Belle Arti 41, 40124 BO. > > > > > ________________________________ > Da: Christian Arnold <chrarnold at web.de> > A: r-help at r-project.org > Inviato: Marted?? 9 dicembre 2008, 21:54:23 > Oggetto: [R] Significance of slopes > > Hello R community, > > I have a question regarding correlation and regression analysis. I havetwo> variables, x and y. Both have a standard deviation of 1; thus,correlation and> slope from the linear regression (which also must have an intercept ofzero) are equal.> I want to probe two particular questions: > 1) Is the slope significantly different from zero? This should be easywith> the lm function, as the p-value should reflect exactly that question. IfI am> wrong, lease correct me. > 2) Is the slope significantly different from a non-zero value (e.g.0.5)? How> can I probe that hypothesis? Any ideas? > > I apologize if this question is too trivial and already answeredsomewhere,> but I did not find it. > > [[elided Yahoo spam]] > Christian > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. > > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code.