An insurance agent has selected a sample of drivers that she insures whose ages are in the range from 16 to 42
years. For each driver, she records the age of the driver (x) and the dollar amount of claims (y) that the driver filed in the previous 12 months. A scatterplot showing the dollar amount of claims as the response and the age as the predictor shows a linear trend. The least squares regression line is determined to be: ˆy = 3715−75.4x. A plot of the residuals versus age of the drivers showed no pattern, and the following were reported: r 2 = 0.822, standard deviation of the residuals Se = 312.1.
. Which of the following is false? (a) 82.2% of the variation in the dollar amounts of claims is explained by the age of the driver. (b) The correlation r between the response and the predictor is 0.907 (c) If the histogram of the residuals is symmetric around zero and bell-shaped, then about 68% of the dollar amounts of claims are within 312.1 dollars of the regression line. (d) A driver in the data set whose age is 25 years had a residual of −$150 using the fitted line above; this means his dollar amount of claims is $1,680.