Question

9.19 Social Networks and Brain Structure A recent study in Great Britain4 examines the relationship between the number of friends an individual has on Facebook and grey matter density in the areas (c) 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 mat (d ter density in the relevant regions) and FBfriends "Kanai, R., Bahrami, B., Roylance, R., and Rees, G., "Online social network size is reflected in human brain structure," Pro- ceedings of the Royal Society, 2012; 279(1732): 1327-1334. Data approximated from information in the article. Facebook). The study London. A (the number of friends on included 40 students at City University scatterplot of the dsta is shown in Figure 9.9 and is shputer output for both cornelation and regression shown below. 26.35 1382 0.000 Mdensity82.452258 2.39 00 300 Figure 9.9 Does brain density ingfiuence mumber of Facebook friends? (a) Use the scatterplot to determine whether any of the study participants had grey matter den- sity scores more than two standard deviations from the mean. (Hint: The grey matter density scores used in the scatterplot are z-scores!) If so, in each case, indicate if the grey matter den sity score is above or below the mean and esti- mate the number of Facebook friends for the individual. (b) Use the scatterplot to determine whether we should have any significant concerns about the conditions being met for using a linear model with these data. (c) What is the correlation between these two vari- ables? What is the p-value from a test of the correlation? What is the conclusion of the test, in context? (d) What is the least squares line to predict the num ber of Facebook friends based on the normal- ized grey matter density score? What number of Facebook friends is predicted for a person whose normalized score is 0? Whose normalized score is +1? Whose normalized score is -1? (e) What is the p-value for a test of the slope? Com pare it to the p-value for the test of correlation. (f) What is R2 for this linear model? Interpret it in context.

Answer 1

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