Regression coefficients
Regression coefficients
- A researcher fitted an educational attainment model
S = β1 + β2ASVABC + β3S M + β4SF + u,
by regressing S, a measure of years of schooling (highest grade completed), on ASVABC, a measure of cognitive ability, SM, and SF, years of schooling (highest grade completed) of the respondents mother and father, respectively. The following output is obtained.
| Source | SS df MS | Number of obs = 500
F( 3, 496) = 81.06 |
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| Model | 1235.0519 3 341.55631 | Prob > F = 0.0000 | ||||||
| Residual | 2518.9701 496 5.07856875 | R-squared = 0.3290
Adj R-squared = 0.3249 |
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| Total | 3754.022 499 7.52309018 | Root MSE = 2.2536 | ||||||
| S | Coef. Std. Err. t P>|t| | [95% Conf. Interval] | ||||||
| ASVABC | 1.242527 | .123587 10.05 0.000 | .999708 | 1.485345 | ||||
| SM | .091353 | .0459299 1.99 0.047 | .0011119 | .1815941 | ||||
| SF | .2028911 | .0425117 4.77 0.000 | .1193658 | .2864163 | ||||
| cons | 10.59674 | .6142778 17.25 0.000 | 9.389834 | 11.80365 | ||||
- Give an interpretation of the regression coeffi [10 marks]
- Perform t tests on the coefficients of the variables. For ASVABC, clearly state the null and alternative hypotheses, compute the test statistic, describe the decision rule, and make conclusion in relation to the parameter and variable; for SM and SF, briefly comment on the final conclusion on the significance of the parameter. [15 marks]
- State the null and alternative hypotheses of the F statistic reported in the output. Calculate the F statistic using the explained sum of squares and the residual sum of squares in the regression output, verify that it matches the F statistic in the output, and perform a test of the explanatory power of the equation as a whole. Also calculate the F statistic using R2 and verify that it is the same. [15 marks]
- Write out the fitted model and predict how many years of schooling would be expected for someone with ASVABC = 0.25, S M = 10, and SF = [10 marks]
