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(14 points) The brain on Facebook ~ Researchers were interested in understanding why some individuals engage in online social networking sites more than others. To investigate, they measured the grey matter density in two regions of the brain that are known to be associated with social perception and memory. They also recorded the number of Facebook friends of each study subject. The scatterplot below shows the relationship between these two variables along with the least squares fit. Note that grey matter density has been reported as a standardized z-score for each individual. Do not round in intermediate calculations for this problem. Round your results to 4 decimal places except where indicated below. Facebook Friends 200 300 400 500 600 100 -2 -1 0 1 Grey Matter Density 1. The researchers conducted an ? v . 2.The relationship between measure of grey matter density and number of Facebook friends is ? v and '? v . 3. The explanatory variable is ? v and the response variable is '2 v . Facebook friends and measure of grey density matter is 0.4571 . Measure of grey matter density: mean = -0.0771, standard deviation = 0.9932 Number of Facebook friends: mean = 337.6286, standard deviation = 176.5671 4. The equation for the regression line is y = + x Round your answers to 6 decimal places. 5.Complete the following sentence to interpret the slope of the regression line: An increase of 1.0 in grey matter density corresponds to a/an 7 v of in number of Facebook friends. 6. Subject A has a recorded grey matter density of -1.5. Use the regression equation to estimate the number of Facebook friends for this individual. 7. The number of Facebook friends for Subject A is 168. Complete the following sentence: The residual for Subject A is . This means the number of Facebook friends for Subject A is O A. higher than 0 B. lower than 0 C. the same as the number of Facebook friends predicted by the regression model. 8. Another individual (not included in this data set) has a grey matter density of 2.5. Would it be appropriate to use this linear model to predict the number of Facebook friends for this individual? GA. No, because 547.0393 number of Facebook friends is too large to be a reasonable number of Facebook friends, even for this point. 0 B. Yes, because 2.5 is a reasonable grey matter density for humans. 0 C. No, because 2.5 is beyond the range of the data used to build the regression model. 9. What are the conclusions of this study? Choose all that apply. A. Large grey matter density cause individuals to have larger counts of Facebook friends B. Grey matter density do not correlate to counts of Facebook friends C. Grey matter density correlates to counts of Facebook friends D. Large grey matter density cause individuals to have smaller counts of Facebook friends E. Increasing the grey matter density an individual has will increase the number of Facebook friends they have. F. Increasina the number of Facebook friends an individual has will increase the arev matter densitv thev have
