Question
A statistician wanted to determine if the demographic variables of age, education, and income influence the number of hours of television watched per week. A
A statistician wanted to determine if the demographic variables of age, education, and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate a multiple regression model where:
Y = number of hours of television watched last week
X1 = age
X2 = number of years of education
X3 = income (in $1,000)
The computer output is shown below:
Predictor | Coeff. | St. Dev. | t |
Constant | 22.3 | 10.7 | 2.084 |
X1 | 0.41 | 0.19 | 2.158 |
X2 | -0.29 | 0.13 | -2.231 |
X3 | -0.12 | 0.03 | -4.00 |
R Square = 34.8%
ANOVA
Source of Variation | d.f. | SS | MS | F |
Regression | 3 | 227 | 75.667 | 3.730 |
Error | 21 | 426 | 20.286 | |
Total | 24 | 653 |
Answer the following questions based on the above-provided information.
a) Complete the following multiple regression equation (2 marks):
Estimated Y =
b) Interpret the meaning of the coefficient of determination (4 marks)
c) Interpret the meaning of the slope coefficients for X1and X2 (4 marks).
d) Write down another potential independent variable that could be included in the analysis (2 marks).
e) Calculate the number of hours of television watched last week for a 37 years old viewer, with four years of education and an annual income of $60,000. (2 marks)
f) Is the overall model significant at the 5% level of significance. What does this finding mean? (no need to show the hypothesis testing steps, only provide the interpretation required)(4 marks)
g) which regression coefficients are significant at the 5% level of significance. What does this finding mean? (no need to show the hypothesis testing steps, only provide the interpretation required) (4 marks)
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