A hockey fan was interested in predicting standings points (points) awarded to teams based on the difference in offensive and defensive scoring rates (differential) for teams in the NHL. 2016- 2017 data was obtained for teams in the eastern conference and is provided in the following table. Note that r = 0.9378 for this data.

Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Pts 65 58 56 55 52 50 49 49 72 68 65 63 56 51 49 49 56.6875 7.6657

Diff 25 4 -4 12 -21 -10 -18 -21 54 46 31 38 -15 0 -14 -31 4.75 26.5393

(a) Identify the explanatory and response variables.

(b) Calculate the least squares regression line using formulas. A calculator may be used to check the results if desired. Report your line in context.

(c) Interpret the slope in terms of the problem.

(d) Interpret the intercept in terms of the problem. Is the interpretation appropriate? Explain.

(e) Use the line to predict the standings points awarded for a differential of zero.

(f) Find the residual for the team that had a differential of zero.

(g) What proportion of variation in points awarded can be explained by the line? Based on this, are you comfortable using the line for prediction? Why or why not?