Frozen pizzas account for over $3 billion/year in sales and are a major sector o
ID: 3134814 • 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 1. For a cheese pizza, if Fat is unchanged, each additional calorie changes the pizza's score by how much?
Question 2. For a pepperoni pizza, if Fat is unchanged, each additional calorie changes the pizza's score by how much?
Question 3. What is the residual for a DiGiorno cheese pizza?
Question 4. 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
Residuals 30 20 10 CheePepp Cheese Pepperoni 0 -10 -20 100 80 60 Pred. Values 40Explanation / Answer
the regression equaion is given by
score=-464.5+1.92*calories-10.38*fat+183.63*Type-0.46*(type*calories)
answer of question 1) here type=1,caloreis=1,type*calories=1, fat is unchanged
change in score will be=1.92+183.63*1-0.46=185.09
answer of question 2)here type=0,caloreis=1,type*calories=0, fat is unchanged
change in score will be=1.92+183.63*0-0.46*0=1.92
anser of question 3) here observed value=85, calories=332, fat=12,type=1,type*calories=332
we fit this value in followin equaion
score=-464.5+1.92*calories-10.38*fat+183.63*Type-0.46*(type*calories)
and estimated score=-464.5+1.92*332-10.38*12+183.63*1-0.46*332=79.29
residual=obserd-estimated=85-79.29=5.71
answer of question 4)
here observed value=85, calories=369, fat=16,type=0,type*calories=0
we fit this value in followin equaion
score=-464.5+1.92*calories-10.38*fat+183.63*Type-0.46*(type*calories)
and estimated score=-464.5+1.92*369-10.38*16+183.63*0-0.46*0=77.9
observed value=85
residual=observed-estimated=85-77.9=7.1
Estimate Standard
Error t Value Pr > |t| Intercept 1 -464.49766 74.72659 -6.22 <.0001 Calories 1 1.92005 0.28424 6.76 <.0001 Fat 1 -10.38466 1.77866 -5.84 <.0001 Type 1 183.63361 59.99236 3.06 0.0057 Type*Calories 1 -0.46150 0.17396 -2.65 0.0145
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