a. Figure 8-5b shows the points from Figure 8-5a with a dashed line at y = , the average

Chapter 8, Problem R.2

(choose chapter or problem)

a. Figure 8-5b shows the points from Figure 8-5a with a dashed line at y = , the average of the y-values of the data. Calculate to show that the figure is correct. b. Calculate x. Show algebraically that the point ( , ) is on the regression line = 1.6x + 0.9 from R1. c. On a copy of Figure 8-5b, sketch both the deviation from the average for the point where x = 9 and the residual (that is, the residual deviation) for this point. Why do you suppose the word residual, which is an adjective, is used as a noun in this instance? the deviations. Why do you suppose that SSdev is so much larger than SSres? Figure 8-5b e. Calculate the coefficient of determination, Then run a linear regression on the points in R1, thus showing that the fraction equals r2. Show that it agrees with the value from the regression on your grapher. Why must you choose the positive square root? g. Figures 8-5c through 8-5f show the ellipses in which the clouds of data points lie. For each graph, tell whether the correlation coefficient is positive or negative and whether it is closer to 0 or closer to 1 or 1. Figure 8-5c Figure 8-5d Figure 8-5e Figure 8-5f