A snack food manufacturer is testing a new snack. Their marketing department ask
ID: 3047523 • Letter: A
Question
A snack food manufacturer is testing a new snack. Their marketing department asks sixteen consumers to rate the moisture content and sweetness on a one to ten scale and rate the taste on a one to one-hundred scale. The table below shows the results of their testing.
a. Calculate the two predictive factor model for the prediction of the enjoyment rating.
b. Which has the greater impact on the differences on the level of enjoyment, the rating of moisture or the rating of sweetness?
Moisture Sweetness Enjoyment Content Measure Rating 4 2 40 4 3 37 4 6 54 4 5 52 6 8 74 6 7 68 6 9 80 6 3 56 8 5 72 8 10 99 8 10 98 8 6 75 10 5 87 10 8 95 10 7 92 10 1 67Explanation / Answer
Answer:
A snack food manufacturer is testing a new snack. Their marketing department asks sixteen consumers to rate the moisture content and sweetness on a one to ten scale and rate the taste on a one to one-hundred scale. The table below shows the results of their testing.
The two models are
Enjoyment Rating = 24.375+6.75* Moisture Content
Enjoyment Rating = 39.4173+5.4245* sweetness measure
Regression Analysis
r²
0.617
n
16
r
0.786
k
1
Std. Error
12.702
Dep. Var.
Enjoyment Rating
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,645.0000
1
3,645.0000
22.59
.0003
Residual
2,258.7500
14
161.3393
Total
5,903.7500
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
24.3750
10.4357
2.336
.0349
1.9926
46.7574
Moisture Content
6.7500
1.4201
4.753
.0003
3.7041
9.7959
Regression Analysis
r²
0.563
n
16
r
0.750
k
1
Std. Error
13.577
Dep. Var.
Enjoyment Rating
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,323.1601
1
3,323.1601
18.03
.0008
Residual
2,580.5899
14
184.3279
Total
5,903.7500
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
39.4173
8.3102
4.743
.0003
21.5937
57.2408
Sweetness Measure
5.4245
1.2775
4.246
.0008
2.6844
8.1645
b. Which has the greater impact on the differences on the level of enjoyment, the rating of moisture or the rating of sweetness?
Moisture content explains 61.7% of variation in enjoyment rating
Sweetness measure explains 56.3% of variation in enjoyment rating
Therefore Moisture content more impact on enjoyment rating.
Regression Analysis
r²
0.617
n
16
r
0.786
k
1
Std. Error
12.702
Dep. Var.
Enjoyment Rating
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,645.0000
1
3,645.0000
22.59
.0003
Residual
2,258.7500
14
161.3393
Total
5,903.7500
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
24.3750
10.4357
2.336
.0349
1.9926
46.7574
Moisture Content
6.7500
1.4201
4.753
.0003
3.7041
9.7959
Regression Analysis
r²
0.563
n
16
r
0.750
k
1
Std. Error
13.577
Dep. Var.
Enjoyment Rating
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,323.1601
1
3,323.1601
18.03
.0008
Residual
2,580.5899
14
184.3279
Total
5,903.7500
15
Regression output
confidence interval
variables
coefficients
std. error
t (df=14)
p-value
95% lower
95% upper
Intercept
39.4173
8.3102
4.743
.0003
21.5937
57.2408
Sweetness Measure
5.4245
1.2775
4.246
.0008
2.6844
8.1645
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