1. Regress the X3 Overall GPA computed, honors-weighted (X3TGPAWGT) variable on the X1 Mathematics standardized theta score (X1TXMTSCOR) (2.5).
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.9212385 | 0.321723 | 2.863453 | 0.0047121 |
| X1TXMTSCOR | 0.0401309 | 0.006166 | 6.508370 | 0.0000000 |
2. Provide a narrative interpretation of the relationship between the coefficient on the X1 Mathematics standardized theta score (X1TXMTSCOR) (2.5).
As X1 Mathematics standardized theta score increases by one point, we can expect X3 Overall GPA to increase by .04 points (p < 0.001).
3. Report the 95% confidence interval for the X1 Mathematics standardized theta score (X1TXMTSCOR) from question 1 and explain the relevance of its inclusion or exclusion of the value 0 (2.5).
| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 0.9212385 | 0.321723 | 2.863453 | 0.0047121 | 0.2862049 | 1.5562721 |
| X1TXMTSCOR | 0.0401309 | 0.006166 | 6.508370 | 0.0000000 | 0.0279601 | 0.0523018 |
The 95% confidence interval is CI(.028, .052) . It is important to inclde the CI because it tells us that the range of plausible estimates does not include 0. In other words, there is a statistically significant relationship between the two variables.
4. What is the rationale to prefer reporting of confidence intervals vs coefficient values (point estimates) (2.5)?
Reporting only the coefficient is misleading and only provides information about the relationship in your sample. On the other hand, reporting the confidence interval gives more detail but letting us know if 0 was a possible estimate for the relationship between the variables as well as the direction of the relationship, positive or negative. If \(b_1 = 0\), then it is possible that you found no meaningful relationship. In general, confidence intervals also clue us in on practical significance.
5. Regress the X3 Overall GPA computed, honors-weighted (X3TGPAWGT) variable on the X1 Mathematics standardized theta score (X1TXMTSCOR) and X1 Scale of student’s mathematics utility (X1MTHUTI) (2.5).
| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 0.7250273 | 0.3570869 | 2.030395 | 0.0440486 | 0.0195699 | 1.4304848 |
| X1TXMTSCOR | 0.0438075 | 0.0067982 | 6.443977 | 0.0000000 | 0.0303770 | 0.0572380 |
| X1MTHUTI | -0.1089527 | 0.0614904 | -1.771865 | 0.0784075 | -0.2304326 | 0.0125271 |
6. Provide a narrative interpretation of the relationship between the coefficient on the X1 Mathematics standardized theta score (X1TXMTSCOR) (2.5).
As X1 Mathematics standardized theta score increases by 1 point, we can expect X3 Overall GPA to increase by .04 points (p < 0.001) holding the other variable constant.
7. Provide a narrative interpretation of the relationship between the coefficient on the X1 Scale of student’s mathematics utility (X1MTHUTI) (2.5).
We cannot conclude that there is a relationship between X3TGPAWGT and X1MTHUTI in our model (p=.08).
8. Regress the X3 Overall GPA computed, honors-weighted (X3TGPAWGT) variable on the X1 Mathematics standardized theta score (X1TXMTSCOR), X1 Scale of student’s mathematics utility (X1MTHUTI), and X1 Socio-economic status composite (X1SES) (2.5).
| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 1.2235357 | 0.3471316 | 3.524703 | 0.0005605 | 0.5377099 | 1.9093616 |
| X1TXMTSCOR | 0.0340752 | 0.0066229 | 5.145040 | 0.0000008 | 0.0209903 | 0.0471600 |
| X1MTHUTI | -0.1011872 | 0.0572444 | -1.767633 | 0.0791287 | -0.2142847 | 0.0119103 |
| X1SES | 0.3843883 | 0.0773896 | 4.966922 | 0.0000018 | 0.2314901 | 0.5372865 |
9. Provide a narrative interpretation of the relationship between the coefficient on the X1 Socio-economic status composite (X1SES) (2.5).
As X1 Socio-economic status increases by one point, we can expect GPA to increase by 0.38 points (p<0.001), holding all other variables in the model constant.
10. How should one interpret a change in the coefficient on X1 Mathematics standardized theta score (X1TXMTSCOR) from the model generated in question 1 vs the model generated in question 8 (2.5)?
The X1TXMTSCOR coefficient decreased from .040 to .034 after we added X1SES to the model. This means that some of the relationship between gpa and math score can be explained by by SES.