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.

You can get the data as an SPSS data file here.

Exercise 2.1. Fit two separate regression models,

1. predicting the child’s MLU from mother’s (Note that this reverses direction of the prediction in comparison to the model in Exercise 1).
2. 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 to decide for the better model fit?

Exercise 2.2. 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.

Include relevant graphics in the SPSS output to inspect whether the residuals are normally distributed or not, and whether residual variance is constant.

1. Does Model 3 fit the data better than previous models?
2. Briefly interpret the graphs you plotted for detecting non-normality and non-constant residual variance.
3. How do you interpret the coefficients of Model 3?
4. Which coefficient estimates are statistically significant (at α = 0.05)?
5. 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?