Question

In a survey, a statistician analyzed the relationship between the Mothers-Heights (explanatory variable 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 ˆy1 = 29.9, and at x2 = 1 the predicted response is ˆy2 = 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