Question

Refer to the following regression output:

Predictor	Coef		SE Coef
Constant	30.00		13.70
X1	-7.00		3.60
X2	3.00		9.30
X3	-19.00		10.80
Source	DF		SS	MS	F
Regression	3.00		8,200.00
Error	25.00
Total	28.00		10,000.00

a. What is the regression equation? (Round the final answers to the nearest whole number. Negative answer should be indicated by a minus sign.)

Y′ =  +   X₁ +  X₂ +  X₃

b. If X₁ = 4, X₂ = 6, and X₃ = 8, what is the value of the dependent variable? (Round the final answer to the nearest whole. Negative answer should be indicated by a minus sign.)

Y′ =

c-1. How large is the sample?

Sample size           

c-2. How many independent variables are there?

Quantity of independent variables           

d. Complete the ANOVA table. (Round the final answers to 2 decimal places.)

	Source	DF	SS	MS	F
	Regression	3	8,200.00
	Error	25
	Total	28	10,000.00

e-1. Conduct a global test of hypothesis, using the 0.05 significance level. (Round the final answers to 2 decimal places.)

H₀: β₁ = β₂ = β₃ = 0

H₁: Not all β's are 0

Reject H₀ if F >             .

The value of the test statistic is             .

f-1. Conduct a test of hypothesis on each of the regression coefficients. (Round the final answers to 3 decimal places. Negative answer should be indicated by a minus sign.)

For X1	For X2	For X3
H0: β1 = 0	H0: β2 = 0	H0: β3 = 0
H1: β1 ≠ 0	H1: β2 ≠ 0	H1: β3 ≠ 0

Reject H₀ if t >  or t <  .

f-2. Compute the values of the test statistic. (Round the final answers to 2 decimal places. Negative answer should be indicated by a minus sign.)

	Test statistic
X1
X2
X3

Answer 1

a)Yhat=30+(-7)*x1+3*x2+(-19)*x3

b)

Yhat=30+(-7)*4+3*6+(-19)*8= -132

c-1) Sample size =28+1=29

c-2) independent variables =3

d)

Source	DF	SS	MS	F
Regression	3	8200	2733.33	37.96
Error	25	1,800.00	72.00
Total	28	10,000.00

e-1)

Reject H₀ if F > 2.99

The value of the test statistic is 37.96

f-1) Reject H₀ if t >2.060 or t <-2.060

Predictor				test statistic
X1				-1.94
X2				0.32
X3				-1.76