5. An insurance company runs a regression on the amount of insurance (in thousands) carried by a household as a function of that household's annual income in thousands). The underlying sample is such that the average income among all households is 74, while the average amount of insurance carried is 223.91. Further, the insurance company predicts that a household earning $100,000 annually will hold $300,350 worth of insurance (ie, Income = 100 suggests that Insurance = 300.35). (a) Determine the regression line used by the insurance company. (b) () Use the regression line from part (a) to estimate the mean amount of insurance held among all households that earn $85,000 annually. (ii) Now consider the mean amount of insurance held among households earning $120,000 annually. By using the regression line for our estimates, do we anticipate this amount to be higher or lower as compared to households earning $150,000 annually? Do we anticipate the variance of the amount of insurance held for such households to be higher or lower as compared to the variance for households earning $150,000 annually? Please explain. (iii) Again consider all houscholds earning $120,000. Does our regression line assume that there are more such households in the population with an insurance amount of $368,000 or with an insurance amount of $345,000? Please explain. (Hint: What assumption does a regression line make about error terms?) ) (i) Suppose the 'true' regression line is such that B) = 3.5 and B2 = 2.9. Consider the sample which generated the regression line in part (a). Would the MSE be higher or lower when this sample is applied to the 'true' regression line or when it is applied to the regression line of part (a)? Please explain. (ii) True or False. Consider three households with associated (Income, Insurance) points (i.c., (X, Y) observations): (47, Y.), (89, Y2) and (112, Y3). Then, under the linear model assumptions, we assume Y, Y2 and Y3 all lie on the same line. Please explain