Regression Analysis of Retail Sales Researchers are investigating the characteristics that may play a role in determining differences in per capita retail sales among different Standard Metropolitan Statistical Areas (SMSA). They collected data on a simple random sample of 25 SMSA, and would like to use regression to relate retail sales, y : Per capita retail sales ($1000s), to the following variables: * : Per capita retail establishments * : Per capita income ($1000s) : Per capita federal expenditures ($1000s) * : Number of males per 100 females Senior data scientist hypothesizes the following first order model: y = Bo + Bix, + Byx, + Byxs + Box, + E a) (2 point) Using the software package, construct scatterplots for y and X1: y and x2: y and x;, and y and x, . Attach your scatterplots. Interpret the scatterplots using correlation coefficient. b) (3 points) Using the software package, estimate the unknown parameters ,: B,: B,. B, and B . Report your least squares prediction equation. Attach your output. c) (2 points) Is there sufficient evidence that the overall model is useful for predicting per capita retail sales? Test using or = 0.05. Attach the portion of the output that is required to do this test. d) (2 points) Test the hypothesis that per capita retail sales decrease as per capita federal expenditures