a .05 level of significance. (Hint: Test for any significant differences due to programs, sex, and interaction. For each test, give the null and alternative hypotheses, test statistics, and conclusion.)

2.4 (10%) Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X₁ in years), level of education (X₂ ranging from 1 to 5), and the person's gender (X₃ where 0=female and 1=male). The following is a partial result of computer output that was used on a sample of 20 individuals.

| ANOVA | | | | |
| --- | --- | --- | --- | --- |
| | df | SS | MS | F |
| Regression | | 84 | | |
| Residual | | 112 | | |
| Predictor | Coefficients | Standard Error of Coefficient | | |
| Constant | 21.00 | 0.70 | | |
| X₁ | 0.62 | 0.10 | | |
| X₂ | 0.92 | 0.19 | | |
| X₃ | -0.51 | 0.92 | | |

(a) \((2\%)\) Present the estimated regression equation and compute the coefficient of determination. Explain it.