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Question
A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3are measured in thousands of dollars. The following results were obtained.| ANOVA | ||||
| df | SS | MS | F | |
| Regression | 3 | 45.9634 | 64.28 | |
| Error | 11 | 2.6218 | ||
| Coefficients | Standard Error | |||
| Intercept | 0.0136 | |||
| x1 | 0.7992 | 0.074 | ||
| x2 | 0.2280 | 0.190 | ||
| x3 | -0.5796 | 0.920 |
Coefficient of determination = 0.946
a. Write out the estimated regression equation for the relationship between the variables.
b. What can you say about the strength of this relationship?
c. Carry out a test of whether yis significantly related to the independent variables. Use a .05 level of significance.
d. Carry out a test to see if x3and yare significantly related. Use a .05 level of significance.
e. Why would a coefficient of determination very close to 1.0 be expected here?
Answer
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