The following table contains the ACT scores and the GPA (grade point average) for three college...
The following table contains the ACT scores and the GPA (grade point average) for three college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Estimate the relationship between GPA and ACT using OLS. Consider the slope estimate (beta1_hat) in equation GPA_hat=beta0_hat+beta1_hat*ACT. Is the relationship between GAP and ACT positive or negative?
| Student | GPA | ACT |
| 1 | 2.8 | 21 |
| 2 | 3.4 | 24 |
| 3 | 3.0 | 26 |
Homework Answers
Following is the regression output using Excel.
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.4336 | |||||
| R Square | 0.1880 | |||||
| Adjusted R Square | -0.6241 | |||||
| Standard Error | 0.3893 | |||||
| Observations | 3 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 0.0351 | 0.0351 | 0.2315 | 0.7145 | |
| Residual | 1 | 0.1516 | 0.1516 | |||
| Total | 2 | 0.1867 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 1.8211 | 2.5987 | 0.7008 | 0.6109 | -31.1986 | 34.8407 |
| ACT | 0.0526 | 0.1094 | 0.4811 | 0.7145 | -1.3373 | 1.4426 |
Regression equation:
GPA = 1.8211 + 0.0526 x ACT
Since coefficient of ACT is positive, it means that relationship between GPA and ACT is positive.
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