Dear members of the R-help list, I have sent the email below to the R-SIG-ME list to ask for help in interpreting some R output of fitted linear models.
Unfortunately, I haven't yet received any answers. As I am not sure if my email was sent successfully to the mailing list I am asking for help here: Dear members of the R-SIG-ME list, I am new to linear models and struggling with interpreting some of the R output but hope to get some advice from here. I created the following dummy data set: scores <- c(2,6,10,12,14,20) weight <- c(60,70,80,75,80,85) height <- c(180,180,190,180,180,180) The scores of a game/match should be dependent on the weight of the player but not on the height. For me the output of the following two linear models make sense: > (lm1 <- summary(lm(scores ~ weight))) Call: lm(formula = scores ~ weight) Residuals: 1 2 3 4 5 6 1.08333 -1.41667 -3.91667 1.33333 0.08333 2.83333 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -38.0833 10.0394 -3.793 0.01921 * weight 0.6500 0.1331 4.885 0.00813 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 2.661 on 4 degrees of freedom Multiple R-squared: 0.8564, Adjusted R-squared: 0.8205 F-statistic: 23.86 on 1 and 4 DF, p-value: 0.008134 > > (lm2 <- summary(lm(scores ~ height))) Call: lm(formula = scores ~ height) Residuals: 1 2 3 4 5 6 -8.800e+00 -4.800e+00 1.377e-14 1.200e+00 3.200e+00 9.200e+00 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 25.2000 139.6175 0.180 0.866 height -0.0800 0.7684 -0.104 0.922 Residual standard error: 7.014 on 4 degrees of freedom Multiple R-squared: 0.002703, Adjusted R-squared: -0.2466 F-statistic: 0.01084 on 1 and 4 DF, p-value: 0.9221 The p-value of the first output is 0.008134 which makes sense as scores and weight have a high correlation and therefore, the scores "can be explained" by the explanatory variable/factor weight very well. Hence, the R-squared value is close to 1. For the second example it also makes sense that the p-value is almost 1 (p=0.9221) as there is hardly any correlation between scores and height. What is not clear to me is shown in my 3rd linear model which includes both weight and height. > (lm3 <- summary(lm(scores ~ weight + height))) Call: lm(formula = scores ~ weight + height) Residuals: 1 2 3 4 5 6 1.189e+00 -1.946e+00 -2.165e-15 4.865e-01 -1.081e+00 1.351e+00 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 49.45946 33.50261 1.476 0.23635 weight 0.71351 0.08716 8.186 0.00381 ** height -0.50811 0.19096 -2.661 0.07628 . --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 1.677 on 3 degrees of freedom Multiple R-squared: 0.9573, Adjusted R-squared: 0.9288 F-statistic: 33.6 on 2 and 3 DF, p-value: 0.008833 It makes sense that the R-squared value is higher when one adds both explanatory variables/factors to the linear model as the more variables are added the more variance is explained and therefore the fit of the model will be better. However, I do NOT understand why the p-value of height (Pr(> | t |) = 0.07628) is now almost significant? And also, I do NOT understand why the overall p-value of 0.008833 is less significant as compared to the one from model lm1 which was p-value: 0.008134. The p-value of weight being low (p=0.00381) makes sense as this factor "explains" the scores very well. After fitting the 3 models (lm1, lm2 and lm3) I wanted to compare model lm1 with lm3 using the anova function to check whether the factor height significantly improves the model. In other words I wanted to check if adding height to the model helps explaining the scores of the players. The output of the anova looks as follows: > lm1 <- lm(scores ~ weight) > > lm2 <- lm(scores ~ weight + height) > > anova(lm1,lm2) Analysis of Variance Table Model 1: scores ~ weight Model 2: scores ~ weight + height Res.Df RSS Df Sum of Sq F Pr(>F) 1 4 28.3333 2 3 8.4324 1 19.901 7.0801 0.07628 . --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 In my opinion the p-value should be almost 1 and not close to significance (0.07) as we have seen from model lm2 height does not at all "explain" the scores. Here, I thought that a significant p-value means that the factor height adds significant value to the model. I would be very grateful if anyone could help me in interpreting the R output. Best regards -- View this message in context: http://r.789695.n4.nabble.com/Help-needed-in-interpreting-linear-models-tp4291670p4291670.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ 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.