Question

# Refer to the following regression output: Predictor Coef SE Coef Constant    30.00 13.70 X1    -7.00 3.60...

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

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