Refer to the following regression output:
Predictor | Coef | SE Coef | |||
Constant | 30.00 | 13.70 | |||
X_{1} | -7.00 | 3.60 | |||
X_{2} | 3.00 | 9.30 | |||
X_{3} | -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′ = + X_{1} + X_{2} + X_{3}
b. If X_{1} = 4, X_{2} = 6, and X_{3} = 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.)
H_{0}: β_{1} = β_{2} = β_{3} = 0
H_{1}: Not all β's are 0
Reject H_{0} 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 X_{1} | For X_{2} | For X_{3} |
H_{0}: β_{1} = 0 | H_{0}: β_{2} = 0 | H_{0}: β_{3} = 0 |
H_{1}: β_{1} ≠ 0 | H_{1}: β_{2} ≠ 0 | H_{1}: β_{3} ≠ 0 |
Reject H_{0} 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 | |
X_{1} | |
X_{2} | |
X_{3} |
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 H_{0} if F > 2.99
The value of the test statistic is 37.96
f-1) Reject H_{0} if t >2.060 or t <-2.060
Predictor | test statistic | |||
X_{1} | -1.94 | |||
X_{2} | 0.32 | |||
X_{3} | -1.76 |
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