A fast food restaurant had a multiple regression performed on some of the nutrit
ID: 2923022 • Letter: A
Question
A fast food restaurant had a multiple regression performed on some of the nutritional information in its menu. The multiple regression was performed to predict calories from Protein content (g), Total Fat (g), Carbohydrate (g), and Sodium (mg) per serving. Use the multiple regression output given below to complete.
1) Do you think this model would do a good job of predicting calories for new menu items? Why or why not?
A.With an R2value of 99.6%, it does not look like this model would do a good job of predicting calories for new menu items.
B. With an R2value of 99.6%, it looks like this model would do a good job of predicting calories for new menu items.
C. Since all of the coefficients for the predictor variables are greater than zero, it looks like this model would do a good job of predicting calories for new menu items.
D.Since all of the coefficients for the predictor variables are greater than zero, it does not look like this model would do a good job of predicting calories for new menu items.
2) The mean of calories is 440.6 with a standard deviation of 229.9 . Discuss what the value of s in the regression means about how well the model fits the data.
A.
The value of s is very small compared with the initial standard deviation of Calories. This indicates that the model fits the data quite well, leaving very little variation unaccounted for.
B.
The value of the mean square regression is very large compared with the initial standard deviation of Calories. This indicates that the model fits the data quite well, leaving very little variation unaccounted for.
C.
The value of the mean square regression is very large compared with the initial standard deviation of Calories. This indicates that the model would does not fit the data very well.
D.
The value of s is very small compared with the initial standard deviation of Calories. This indicates that the model would does not fit the data very well.
3) Does the r^2 value of 99.6% mean that the residuals are all actually equal to zero? How can you tell this from the table?
A.
No, the residuals are not all zero. The standard deviation, s, is greater than zero, which indicates that there is some variation in the predicted values.
B.
Yes, the residuals are all equal to zero. The coefficients are greater than zero, which indicates that there is no variation in the predicted values.
C.
No, the residuals are not all zero. The coefficients are greater than zero, which indicates that there is some variation in the predicted values.
D.
Yes, the residuals are all equal to zero. The standard deviation, s, is greater than zero, which indicates that there is no variation in the predicted values.
Dependent variable is: Pct BF
R-squared=99.6%
R-squared (adjusted)equals=99.6%
s=8.54 with 1115=106 degrees of freedom
Source
Sum of Squares
df
Mean Square
F-ratio
Regression
4750466
4
1187617
16394
Residual
7678.85
106
72.4420
Variable
Coefficient
SE(Coeff)
t-Ratio
P-value
Intercept
-5.736
2.597
2.21
0.0293
Protein
3.8241
0.0909
42.07
<0.0001
Total fat
9.2552
0.0847
109.27
<0.0001
Carbs
3.8106
0.0407
93.63
<0.0001
Na/Serv.
1.2339
0.4471
2.76
0.0068
Source
Sum of Squares
df
Mean Square
F-ratio
Regression
4750466
4
1187617
16394
Residual
7678.85
106
72.4420
Explanation / Answer
Que 1
Answer B :with an R2 value of 99.6% it looks like this model would do a good job of predicting calories of new food item
Que 2
Answer :A: the value of s is very small compared with the initial standard deviation of calories . This indicates that the model fits the data quiet well , leaving very little variation unaccounted for.
Question 3:
Answer: A: no the residuals are not all zero. The standard deviation s is greater than zero which indiactes that there is some variation inthe predicted value.
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