Suppose we want to understand the relationship between Fat content (X1) and Saturated Fat content (X2) on the Calories of 13 hot dog brands. We wish to build a multiple linear model for these data, based on the below summary values: 13 13 13 13 Xi1 = 151, 789, >Yi = 1760

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Multiple linear regression 

b) 

Suppose we want to understand the relationship between Fat content (X1) and Saturated Fat
content (X2) on the Calories of 13 hot dog brands. We wish to build a multiple linear model for
these data, based on the below summary values:
13
13
13
13
> Til
151, Ci2
= 63, > X;1X¿2
789,
Yi
1760
i=1
i=1
i=1
i=1
13
13
13
13
21650,
Xi2Yi
9040,
x = 1887, x = 331
Xi1Yi
i=1
i=1
i=1
i=1
(a)
sary inverse matrix, but should show all other steps in your work.
Estimate the fitted regression coefficients. You may use software to find the neces-
(b)
Interpret the coefficient of Fat in the context of the data.
(c)
of squares for this model is 313.6.
Find a 95% confidence interval for the slope of Saturated Fat, if the residual sum
(d)
simple linear regression, we derived the sampling distribution to be used in building pre-
diction intervals for a predicted response at the value X = x* by considering instead the
sampling distribut
and distribution for the error in a prediction based on a multiple linear model involving
predictors.
This question is independent of the previous questions. Recall that in
of Y* – ĝ*, the error in our prediction. Determine the mean, variance,
Transcribed Image Text:Suppose we want to understand the relationship between Fat content (X1) and Saturated Fat content (X2) on the Calories of 13 hot dog brands. We wish to build a multiple linear model for these data, based on the below summary values: 13 13 13 13 > Til 151, Ci2 = 63, > X;1X¿2 789, Yi 1760 i=1 i=1 i=1 i=1 13 13 13 13 21650, Xi2Yi 9040, x = 1887, x = 331 Xi1Yi i=1 i=1 i=1 i=1 (a) sary inverse matrix, but should show all other steps in your work. Estimate the fitted regression coefficients. You may use software to find the neces- (b) Interpret the coefficient of Fat in the context of the data. (c) of squares for this model is 313.6. Find a 95% confidence interval for the slope of Saturated Fat, if the residual sum (d) simple linear regression, we derived the sampling distribution to be used in building pre- diction intervals for a predicted response at the value X = x* by considering instead the sampling distribut and distribution for the error in a prediction based on a multiple linear model involving predictors. This question is independent of the previous questions. Recall that in of Y* – ĝ*, the error in our prediction. Determine the mean, variance,
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