Question

Given the following regression output,

Predictor		Coefficient			SE Coefficient			t		p-value
Constant		84.998			1.863			45.62		0.000
x1		2.391			1.200			1.99		0.051
x2		-0.409			0.172			-2.38		0.021

Analysis of Variance
Source	DF		SS		MS		F		p-value
Regression	2		77.907		38.954		4.138		0.021
Residual Error	62		583.693		9.414
Total	64		661.600

answer the following questions:

Write the regression equation. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

y= ____________ + _______________x1 + ________________ x2

If x₁ is 4 and x₂ is 11, what is the expected or predicted value of the dependent variable? (Round your answer to 3 decimal places.)

Dependent variable _______________

How large is the sample? How many independent variables are there?

Sample n _____________

Independent variables k _____________

State the decision rule for 0.05 significance level: H₀: β₁ = β₂ = 0; H₁: Not all β's are 0. (Round your answer to 2 decimal places.)

Reject H0 if F > ___________

Compute the value of the F statistic. (Round your answer to 2 decimal places.)

Computed value of F _____________

What is the conclusion? Use the 0.05 significance level.

REJECT or DO NOT REJECT (CHOOSE) H0. ALL or NOT ALL (choose) net rregression coefficients equal zero.

State he decision rule for each independent variable. Use the 0.05 significance level. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

Reject H0 if t < ___________________ or t > ________________

Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

For X1 _______________

For X2 _______________

Which variable would you consider eliminating?

Delete variable X1 or X2 (choose) and keep X1 or X2. choose)

Outline a strategy for deleting independent variables in this case.

The regression analysis should be repeated with only X1 or X2 (choose) as the independent variable.

Answer 1

The regression equation is

The required predicted value is

Sample n= 64+1 = 65

Independent variables k =2

The critical value of F using excel function "=FINV(0.05,2,62)" is 3.15.

Reject H0 if F > 3.15

Computed value of F = 4.14

What is the conclusion? Use the 0.05 significance level.

REJECT H0. NOT ALL regression coefficients equal zero.

The critical value of t using excel function "=TINV(0.05,62)" is +/- 1.999.

Reject H0 if t < -1.999 or t > 1.999

For X1: t = 1.99

For X2: t = -2.38

Since for X1 t does not lie in rejection region so it is not significant.

Delete variable X1 and keep X2.

The regression analysis should be repeated with only X2 as the independent variable.