1 Simple regression

It is claimed that caregivers adapt their language to the language abilities of children during language acquisition. We follow a particular child and record an hour conversation between the child and her mother once every month between the child’s second and fourth birth dates. We calculate a well-known measure of language complexity/competency mean length of utterance (MLU), for the child and her mother for each recording session. The data is given below.1

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

Exercise 1.1. Draw a scatter plot of Mother’s MLU vs. Child’s MLU. Also draw a fitted regression line over the scatter plot.

Mark or clearly describe the most influential data point in the scatter plot.

Exercise 1.2. Perform a linear regression analysis that predicts the mother’s MLU using the child’s MLU as the predictor. Answer the questions below using the analysis performed.

1. What are the estimated coefficients, intercept (a) and slope (b).
2. Assuming the linear regression model is correct, how do you interpret the values of intercept and the slope?
3. Check whether residuals are normally distributed or not. Which part of the output is useful for answering this question?
4. We hypothesize that caregivers adjust their language based on children’s language proficiency. As a result, we expect the mother’s MLU to increase as the child’s MLU increases.

   State whether this hypothesis is supported or disproved by the regression model at α-level 0.05.

5. What is the rate or percentage of variation in the mother’s MLU explained by the child’s MLU? Which statistics in the output express the explained variance?