Question

The following multiple regression printout can be used to predict a person's height (in inches) given his or her shoe size and gender, where gender = 1 for males and 0 for females.

Regression Analysis: Height Versus Shoe Size, Gender
Coefficients
Term	Coef	SE Coef	T-Value	P-Value
Constant	55.21	1.08	51.12	0.000
Shoe Size	1.167	0.11		0.000
Gender	2.579	0.483	5.34	0.000

(a)

Find the value of the test statistic for shoe size. (Round your answer to two decimal places.)

t =

(b)

Is the regression coefficient of shoe size statistically significant? (Use α = 0.05.)

The regression coefficient of shoe size

statistically significant.

(c)

Does the variable shoe size belong in the model?

The variable shoe size

belong in the model.

(d)

Interpret the regression coefficient of Gender. (Round your answer to 3 decimal places).

Males are inches taller than females, on average, controlling for shoe size.

Answer 1

SOLUTION:

From given data,

The following multiple regression printout can be used to predict a person's height (in inches) given his or her shoe size and gender, where gender = 1 for males and 0 for females.

(a) Find the value of the test statistic for shoe size. (Round your answer to two decimal places.)

We know that ,

Formula for Test Statistic

Test Statistic : t  = / SE()

Where,

= shoe size = 1.167

SE() = 0.11

The test statistic will be t = / SE()  

t = 1.167 / 0.11

t = 10.61

(b) Is the regression coefficient of shoe size statistically significant? (Use α = 0.05.)The regression coefficient of shoe size statistically significant.

We have α = 0.05

Since P-value < 0.05, so we can say

The regression coefficient of shoe size is statistically significant.

(c) Does the variable shoe size belong in the model?

The variable shoe size does belong in the model.

(d) Interpret the regression coefficient of Gender. (Round your answer to 3 decimal places).

Males are 2.579 inches taller than females, on average, controlling for shoe size.