Question
Analyzing Editor Bonuses and Book Series Performance A multinational publishing house is looking to adjust its bonus structure for editors based on the performance of
Analyzing Editor Bonuses and Book Series Performance A multinational publishing house is looking to adjust its bonus structure for editors based on the performance of the books they manage. The company aims to explore the relationship between the performance of a book series and the bonuses awarded to editors. The data from the previous year in the table below: detailing the bonuses received by editors and the yearly percentage increase in sales for each book series they managed. These variables are labeled as Bonuses and SalesGrowth, respectively.
a) Construct a scatter plot for the editors' bonuses (variable Bonuses) against the yearly sales growth (variable Sales Growth). Discuss any observable trends and relationships. Are any outliers or high leverage points present in the dataset?
b) Fit the model below and document your findings. = 0 + 1 +
c) Generate the corresponding residual plot (residuals versus predicted values). Evaluating this plot, does the estimated model seem adequate?
d) Estimate a revised model, now incorporating the adjusted variables Bonuses-Adj and SalesGrowth-Adj, which exclude any data points where editors' bonuses seem disproportionately high relative to the sales growth of their book series. In your findings, you are expected to identify nine data points that are disproportionately high; include these in your response.
e) Create a histogram of the residuals from your regression analysis in part d). Does this model comply with the assumption of approximate normality?
f) What are the measurement units of the slope coefficient b1 in the updated regression model from part d)? How does an increase of 1 percentage point in sales growth affect the average bonus of editors?
g) Compute and elucidate the 2 and Adjusted 2 values for both regression models (parts b and d).
h) Determine a 95% confidence interval for the regression slope 1 in part d).
i) Perform hypothesis testing for the slope coefficient 1 in the model fitted in part b). State your null and alternative hypotheses, calculate the test statistic, and interpret the results.
Bonuses ($) | SalesGrowth (%) |
56940 | 14.1 |
52052 | 10.9 |
58344 | 23.5 |
30056 | 5.9 |
71136 | 13.8 |
59540 | 20.0 |
56056 | 16.4 |
56888 | 16.3 |
64324 | 10.5 |
43316 | 26.3 |
29484 | 25.9 |
48516 | 26.8 |
69628 | 14.8 |
48724 | 22.3 |
104572 | 56.3 |
82420 | 12.6 |
47060 | 20.4 |
55016 | 1.9 |
47944 | 19.9 |
63440 | 15.4 |
53144 | 38.7 |
39468 | 16.4 |
73528 | 24.4 |
54132 | 15.6 |
87776 | 14.4 |
155116 | 19.0 |
60320 | 16.1 |
199888 | 12.1 |
24752 | 16.2 |
77584 | 18.4 |
53248 | 14.2 |
82836 | 14.9 |
22204 | 12.4 |
43108 | 17.1 |
41444 | 16.9 |
30004 | 18.1 |
69784 | 10.9 |
92248 | 19.3 |
36868 | 18.3 |
44720 | 18.4 |
69472 | 13.8 |
26832 | 13.7 |
48412 | 12.7 |
42380 | 15.1 |
87412 | 16.5 |
29536 | 10.2 |
40300 | 19.6 |
61776 | 12.8 |
40664 | 15.9 |
60840 | 17.3 |
76388 | 8.5 |
47632 | 16.4 |
55640 | 19.5 |
46488 | 19.2 |
43108 | 15.9 |
40560 | 19.9 |
121004 | 28.1 |
37284 | 25.0 |
71136 | 15.0 |
105456 | 12.6 |
62140 | 20.3 |
13312 | 22.7 |
40300 | 14.8 |
73164 | 13.2 |
28236 | 10.3 |
45448 | 17.7 |
66924 | 10.0 |
64896 | 15.6 |
45500 | 6.8 |
48100 | 12.4 |
41496 | 13.1 |
39520 | 15.8 |
31200 | 12.8 |
51532 | 15.3 |
81640 | 0.5 |
47372 | 16.5 |
70720 | 15.1 |
36400 | 13.0 |
38532 | 11.1 |
57044 | 8.9 |
49556 | 17.5 |
22932 | 15.9 |
30940 | 14.2 |
55484 | 9.3 |
67496 | 9.5 |
93496 | 15.5 |
215436 | 14.4 |
69472 | 11.1 |
91000 | 15.9 |
47424 | 16.4 |
98384 | 8.6 |
43316 | 24.6 |
59384 | 15.4 |
60268 | 16.9 |
66716 | 7.2 |
109668 | 11.6 |
54028 | 26.4 |
51584 | 21.4 |
65156 | 19.2 |
37492 | 15.1 |
70252 | 9.0 |
72332 | 9.4 |
64740 | 19.0 |
80600 | 3.5 |
111800 | 22.1 |
95992 | 10.9 |
29796 | 15.1 |
345280 | 10.2 |
49868 | 17.3 |
31824 | 33.3 |
94640 | 22.8 |
73372 | 11.1 |
53352 | 12.4 |
66924 | 20.9 |
41600 | 6.7 |
57980 | 7.1 |
84812 | 11.8 |
99320 | 14.0 |
51792 | 10.1 |
47736 | 6.4 |
65572 | 12.4 |
54756 | 17.6 |
63492 | 15.1 |
90376 | 23.6 |
163384 | 35.7 |
98800 | 23.2 |
22204 | 12.4 |
88400 | 44.4 |
18720 | 2.1 |
23868 | 18.4 |
69680 | 16.1 |
37908 | 15.1 |
11596 | 22.7 |
109252 | 23.4 |
56264 | 25.7 |
92612 | 27.0 |
41132 | 19.9 |
108784 | 43.7 |
81796 | 16.4 |
54340 | 11.6 |
88088 | 24.8 |
23556 | 26.2 |
58760 | 44.5 |
69368 | 22.3 |
69888 | 22.3 |
82420 | 35.1 |
101192 | 13.1 |
84188 | 11.0 |
84240 | 19.4 |
50284 | 28.5 |
74412 | 43.9 |
64012 | 26.8 |
40040 | 15.7 |
82888 | 15.0 |
81536 | 28.2 |
51740 | 15.4 |
56004 | 20.0 |
60372 | 42.2 |
72852 | 19.6 |
58604 | 16.2 |
159536 | 21.5 |
37960 | 29.5 |
37908 | 22.6 |
584116 | 22.9 |
49348 | 13.0 |
189592 | 7.8 |
78104 | 48.1 |
41964 | 18.0 |
37076 | 18.0 |
77428 | 21.7 |
38272 | 21.3 |
63752 | 26.9 |
28236 | 30.5 |
770744 | 19.4 |
46280 | 15.6 |
84604 | 19.4 |
125216 | 29.1 |
116896 | 40.8 |
40924 | 13.7 |
24648 | 11.1 |
22828 | 10.8 |
24180 | 5.1 |
30888 | 12.3 |
35776 | 7.4 |
31564 | 6.2 |
32968 | 12.7 |
27664 | 10.6 |
22932 | 7.4 |
36088 | 12.6 |
27040 | 12.8 |
39364 | 2.9 |
34736 | 13.5 |
41756 | 10.7 |
26000 | 11.9 |
28704 | 12.9 |
21424 | 10.1 |
57200 | 7.3 |
49868 | 14.6 |
17316 | 13.8 |
26156 | 8.9 |
23296 | 14.0 |
38064 | 12.9 |
37440 | 14.5 |
42016 | 14.7 |
48360 | 9.0 |
27300 | 15.5 |
34216 | 12.1 |
28860 | 13.7 |
32552 | 14.4 |
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