1) In a certain section of a city, muggings have been a problem. The number of police officers patrolling that section of the city has varied. The following chart shows the number of police officers and the number of muggings for 8 successive days. Police Officers 20 12 18 15 22 10 20 12 Muggings 5 9 10 8 6 13 7 15 a) What is the explanatory variable? What is the response variable? b) What is the least squares regression equation? c) What is the correlation coefficient, r? Interpret this result. d) What is the coefficient of determination, r?? Interpret this result.c) What is the correlation coefficient, r? Interpret this result. d) What is the coefficient of determination, r?? Interpret this result. e) Use the equation in part (b) to estimate the average number of muggings when 16 police officers are patrolling that section of the city.2] Does the weight of a car affect miles per gallon? We would like to determine if there is a linear relationship between weight of a car and miles per gallon ofthe car. Using the Minitab printout below answer the following questions: a} What is the explanatory variable? What is the response variable? b} What is the least squares regression equation? 5] What is the ooefficient of determination, r2? Interpret this result. d} What is the correlation coefficient, r? Interpret this result. e} Are there any:r outliers? If so, which observations are outliers? Are there any influential observations? If so, which observations are influential? f] Suppose the weight of the cars in this sample ranged from 1.95 to 4.35 thousand pounds What would be the predicted miles per gallon of a car weighing 2.5 thousand pounds? What would be the predicted miles per gallon of a car weighting ?.5 thousand pounds? Are there any influential observations? It so, which observations are influential? f) Suppose the weight of the cars in this sample ranged from 1.95 to 4.36 thousand pounds What would be the predicted miles per gallon of a car weighing 2.5 thousand pounds? What would be the predicted miles per gallon of a car weighting 7.5 thousand pounds? Regression Analysis: MPG versus Weight Analysis of Variance Source DE Ass ATMS F-Value P-Value Regression 1293.52 1293.52 0.000 Weight 1293.52 159.16 159.16 0.0DO Error 36 8.13 Lack-of-Fit 34 290 27 854 7.41 0.126 Pure Error 2.31 1.15 Totel 37 1586.09 Model Summary S R-5q R-sqladj) R-sq(pred) 2.85080 81.55% 81.04% 79.57% + Coefficients Term Cool SE Coel T-Value P-Value VIF Constant 48.71 1.95 24.93 0.000 Weight -8.365 0.563 -12.62 D.OOO 1.00 Regression Equation MPG = 48.71 -8.365 Weight Fits and Diagnostics for Unusual Observations Obs MPG Fit Resid Std Resid 5 16.200 29.299 -13.099 -3.86 R 19 33.500 27.328 6.172 2.20 RX 25 37.300 30.891 6.409 2.31 R 32 25.500 23.521 1.979 0.28 X R Large residual
