Exercise 9.19 on page 536 introduces a study examining the relationship between the number of friends an individual has on Facebook and grey matter density in the areas of the brain associated with social perception and associative memory. The data are available in the dataset FacebookFriends and the relevant variables are GMdensity (normalized z-scores of grey matter density in the brain) and FBfriends (the number of friends on Facebook). The study included 40 students at City University London. Computer output for ANOVA for regression to predict the number of Facebook friends from the normalized brain density score is shown below.

Is the linear model effective at predicting the number of Facebook friends? Give the F-statistic from the ANOVA table, the p-value, and state the conclusion in context. (We see in Exercise 9.19 that the conditions are met for fitting a linear model in this situation.)

Exercise 9.19

A recent study in Great Britain examines the relationship between the number of friends an individual has on Facebook and grey matter density in the areas of the brain associated with social perception and associative memory. The data are available in the dataset FacebookFriends and the relevant variables are GM density (normalized z-scores of grey matter density in the relevant regions) and FBfriends (the number of friends on Facebook). The study included 40 students at City University London. A scatterplot of the data is shown in Figure 9.9 and computer output for both correlation and regression is shown below.

Figure 9.9

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The regression equation is FBfriends = 367 + 82.4 GMdensity Analysis of Variance Source Regression Residual Error 38 1043545 Total DF MS 245400 245400 8.94 0.005 27462 1288946 39 Pearson correlation of GMdensity and FBfriends = 0.436 P-Value = 0.005 The regression equation is FBfriends = 367 + 82.4 GMdensity SE Coef 26.35 Predictor Coef P Constant 366.64 13.92 0.000 GMdensity 82.45 27.58 2.99 0.005 S= 165.716 R-Sq = 19.0% R-Sqladj) = 16.9%