2 Multiple regression
In this exercise we will use the same data set we used for simple regression analysis in Exercise 1. Data
is repeated here for your convenience, see Exercise 1 for a description.
Age (months) | Child’s MLU | Mother’s MLU |
25 | 1.46 | 5.42 |
26 | 1.41 | 5.69 |
27 | 1.66 | 6.27 |
28 | 1.74 | 6.10 |
29 | 1.90 | 6.06 |
30 | 1.91 | 5.98 |
31 | 1.85 | 6.10 |
32 | 2.06 | 6.09 |
33 | 2.27 | 6.10 |
34 | 2.43 | 6.14 |
35 | 2.70 | 6.42 |
36 | 2.81 | 6.35 |
37 | 2.69 | 6.21 |
38 | 2.72 | 6.07 |
39 | 2.64 | 5.84 |
40 | 3.05 | 6.17 |
41 | 3.22 | 5.74 |
42 | 3.42 | 6.11 |
43 | 3.70 | 6.41 |
44 | 3.90 | 5.50 |
45 | 3.57 | 6.00 |
46 | 3.49 | 6.90 |
47 | 3.66 | 6.65 |
48 | 3.64 | 6.40 |
|
You can also get the data as an SPSS sav file.
- Fit two separate regression models,
- predicting the child’s MLU from mother’s (Note that this reverses direction of the
prediction in comparison to the model in Exercise 1).
- predicting the child’s MLU from her age.
What are the coefficients (intercept and slope) of each model? Explain briefly how to interpret all
four coefficients you have calculated.
- Which of the two models above fits the data best? Which statistic(s) you use for deciding for the
better model?
- Fit a multiple regression model (Model 3), predicting the child’s MLU from both her age and the
Mother’s MLU. List all coefficients of Model 3.
Does Model 3 fit the data better than previous models?
- Plot relevant graphics to inspect whether
- residuals are normally distributed or not.
- whether residuals are independent.
Report your interpretation of the graphs briefly.
- How do you interpret the coefficients of Model 3?
- Which coefficient estimates are statistically significant (at α = 0.05)?
- How do you explain the differences between the estimates of slopes of individual predictors in
Model 3 and the corresponding coefficients in Model 1 and Model 2?