Question

Exercise 1:

In a survey, a statistician analyzed the relationship between the Mothers-Heights (explanatory vari- able x) and the Daughters-Heights (response y) by using the regression method. When he drew the regression line, he found that at x1 = 0 the predicted response is yˆ1 = 29.9, and at x2 = 1 the predicted response is yˆ2 = 30.43. Answer the following questions providing all the details.

1. Find the intercept a and slope b of the regression line of Daughters-Heights on Mothers-Heights.

2. Use the regression line to predict the height of a Daughter from her Mother-Height = 65.

3. If the standard deviations of Daughters-Heights is sy = 2.6 and Mothers-Heights is sx = 2.35,

   what is the value of the correlation r between the two variables?

4. Does this regression method accurately predict well the Daughters-Heights? Explain.

5. What will happen to the regression line if we add and account for an influential observation?

Answer 1

As the value of r² is so small, so the model does not predict the height of the daughter accurately.

5. If we add influential observation, the regression line tends to be affected and passes close to the influential observation. It will reduce the predictive power of the model further. So, influential observation need to be removed before fitting any regression model.

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