Frozen pizzas account for over $3 billion/year in sales and are a major sector o
ID: 3392993 • Letter: F
Question
Frozen pizzas account for over $3 billion/year in sales and are a major sector of the frozen food market; see Companies and Markets. Consumer's Union recently rated 27 brands of frozen pizza and assigned a score to each brand based on flavor and quality. The data are in this Excel file: Pizza Ratings. A multiple regression with Score as the response variable and Fat, Calories, and Type (cheese = 1, pepperoni = 0) resulted in the following plot of the residuals against the predicted values; the plot has been color-coded by Type of pizza: pizza ratings resid vs pred The plot indicates that there are different slopes for the 2 types of pizza. To adjust the slopes an interaction term should be included in the model. Perform a multiple regression with Score as the response variable and Calories, Fat, Type (cheese = 1, pepperoni = 0) and the interaction term Type*Calories as the explanatory variables.
QUESTION: What is the residual for a DiGiorno pepperoni pizza?
Brand
Score
Cost
Calories
Fat
Type
Type*Calories
Freshetta 4 Cheese
89
0.98
364
15
1
364
Freschetta stuffed crust
86
1.23
334
11
1
334
DiGiorno
85
0.94
332
12
1
332
Amy's organic
81
1.92
341
14
1
341
Safeway
80
0.84
307
9
1
307
Tony's
79
0.96
335
12
1
335
Kroger
75
0.8
292
9
1
292
Tombstone stuffed crust
75
0.96
364
18
1
364
Red Baron
73
0.91
384
20
1
384
Bobli
67
0.89
333
12
1
333
Tombstone extra cheese
60
0.94
328
14
1
328
Jack's
51
0.92
325
13
1
325
Celeste
50
1.17
346
17
1
346
McCain Ellio's
46
0.54
299
9
1
299
Totino's
25
0.67
322
14
1
322
Freschetta pepperoni
89
0.96
385
18
0
0
DiGiorno pepperoni
85
0.88
369
16
0
0
Tombstone stuffed crust pepperoni
80
0.9
400
22
0
0
Tombstone pepperoni
73
0.88
378
20
0
0
Red Baron pepperoni
64
0.89
400
23
0
0
Tony's pepperoni
60
0.87
410
26
0
0
Red Baron deep dish pepperoni
55
1.28
412
25
0
0
Stouffer's pepperoni
54
1.26
343
14
0
0
Weight Watchers pepperoni
33
1.51
283
6
0
0
Jeno's pepperoni
22
0.74
372
20
0
0
Totino's pepperoni
20
0.64
367
20
0
0
Healthy Choice pepperoni
15
1.62
280
4
0
0
Brand
Score
Cost
Calories
Fat
Type
Type*Calories
Freshetta 4 Cheese
89
0.98
364
15
1
364
Freschetta stuffed crust
86
1.23
334
11
1
334
DiGiorno
85
0.94
332
12
1
332
Amy's organic
81
1.92
341
14
1
341
Safeway
80
0.84
307
9
1
307
Tony's
79
0.96
335
12
1
335
Kroger
75
0.8
292
9
1
292
Tombstone stuffed crust
75
0.96
364
18
1
364
Red Baron
73
0.91
384
20
1
384
Bobli
67
0.89
333
12
1
333
Tombstone extra cheese
60
0.94
328
14
1
328
Jack's
51
0.92
325
13
1
325
Celeste
50
1.17
346
17
1
346
McCain Ellio's
46
0.54
299
9
1
299
Totino's
25
0.67
322
14
1
322
Freschetta pepperoni
89
0.96
385
18
0
0
DiGiorno pepperoni
85
0.88
369
16
0
0
Tombstone stuffed crust pepperoni
80
0.9
400
22
0
0
Tombstone pepperoni
73
0.88
378
20
0
0
Red Baron pepperoni
64
0.89
400
23
0
0
Tony's pepperoni
60
0.87
410
26
0
0
Red Baron deep dish pepperoni
55
1.28
412
25
0
0
Stouffer's pepperoni
54
1.26
343
14
0
0
Weight Watchers pepperoni
33
1.51
283
6
0
0
Jeno's pepperoni
22
0.74
372
20
0
0
Totino's pepperoni
20
0.64
367
20
0
0
Healthy Choice pepperoni
15
1.62
280
4
0
0
Explanation / Answer
Here we obtain the multiple linear regresion of Score as the response variable and Calories, Fat, Type (cheese = 1, pepperoni = 0) and the interaction term Type*Calories as the explanatory variables as-
Score = - 464 + 1.92 Calories - 10.4 Fat + 184 Type - 0.461 Type*Calories
Thus the residual for a DiGiorno pepperoni pizza=6.24092
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