Part A- We have a dataset that shows nutritional information for 30 different breakfast cereals. Here is computer output for a four-variable relationship between

Y = Calories and X₁ = Fat, X₂ = Protein and X₃ = Fiber.

Regression Equation

Calories

=

85.01 + 18.56 Fat + 7.54 Protein+ 3.51 Fiber

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
21.4164	66.07%	62.16%	42.39%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	85.01	8.35	10.18	0.000
Fat	18.56	3.71	5.00	0.000	1.05
Protein	7.54	3.05	2.47	0.020	1.36
Fiber	3.51	2.46	1.42	0.166	1.35

Which x variable has the most influence in this multiple linear relationship? In other words, which of these three x variables is the best for predicting y?

A. X₂ = Protein

B. X₁ = Fat

C. X₃ = Fiber

Part B- Data were collected on the age (in years), mileage (in thousands of miles), and price (in thousands of dollars) of a random sample of used Hyundai Elantras. Output is provided.

The regression equation is Price = 15.2 - 0.0101 Mileage - 1.55 Age

Predictor	Coef	SE Coef	T	P
Constant	15.2174	0.6112	24.90	0.000
Mileage	-0.01005	0.01977	-0.51	0.616
Age	-1.5466	0.3508	-4.41	0.000

S = 1.39445 R-Sq = 89.0% R-Sq(adj) = 88.0%

How many explanatory variables are used in this model?

A. 2

B. 1

C. 4

D. 3

Part C- A dataset shows the number of capital letters that a student can write in 15 seconds using the non-dominant hand (X) versus the same thing for the dominant hand (Y). The data is for 63 students. Here is computer output:

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
5.05128	35.69%	34.64%	31.49%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	22.69	2.08	10.92	0.000
nondom	0.876	0.151	5.82	0.000	1.00

Regression Equation

dom

=

22.69 + 0.876 nondom

Using the equation of the line of best fit, predict the number of dominant hand letters a person can write in 15 seconds if they can write 10 letters with the non-dominant hand. This is a point estimate not a confidence interval.