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1 Simple regression

During language acquisition, it is known that caregivers adapt their language to the language abilities of children. We follow a particular child and record an hour conversation between them once every month between their second and fourth birth dates. We calculate a well-known measure of language complexity/competency for children Mean Length of Utterance (MLU), for the child and her mother for each recording sessions. The date is given below.1

Age (months)Child’s MLUMother’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
  1. Draw a scatter plot of Child’s MLU vs. Mother’s MLU. Also draw a fitted regression line over the scatter plot.

    Do you see any suspicious (influential) data points?

  2. Perform a linear regression analysis that predicts the mother’s MLU using the child’s MLU as the predictor variable. Determine the regression coefficients: intercept (a) and slope (b).

    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.
  4. What is the standard errors for the estimates of slope and intercept.
  5. We hypothesize that the 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 by the regression model above at α-level 0.05.

  6. What is the rate or percentage of variation in the mother’s MLU explained by the child’s MLU?

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