3.30. Refer to Sales growth Problem 3.17. a Divide the range of the predictor variable (coded years) into five bands of width 2.0, as follows: Band 1 ranges from X = -.5 to X = 1.5; band 2 ranges from X = 1.5 to X = 8.5; and so on. Determine the median value of X and the median value of Y in each band and develop the band smooth by connecting the five pairs of medians by straight lines on a scatter plot of the data. Does the band smooth suggest that the regression relation is linear? Discuss. b. Create a series of seven overlapping neighborhoods of width 3.0 beginning at X = -.5. The first neighborhood will range from X = -.5 to X = 2.5; the second neighborhood will range from X = .5 to X = 3.5; and so on. For each of the seven overlapping neighborhoods, fit a linear regression function and obtain the fitted value Y, at the center X, of the neighborhood. Develop a simplified version of the lowess smooth by connecting the seven (X., Y.) pairs by straight lines on a scatter plot of the data. c. Obtain the 95 percent confidence band for the true regression line and plot it on the plot prepared in part (b). Does the simplified lowess smooth fall entirely within the confidence band for the regression line? What does this tell you about the appropriateness of the linear regression function