Consider the following data on height (in inches) and number of siblings for a random sample of 10 female students at a large university.

1. Construct a scatterplot of the given data. Does there appear to be a linear relationship between y = height and x = number of siblings?

2. Compute the value of the correlation coefficient. Is the value of the correlation coefficient consistent with your answer from Step 1? Explain.

3. What is the equation of the least-squares line for these data?

4. Is the slope of the least-squares regression line from Step 3 equal to 0? Does this necessarily mean that there is a meaningful relationship between height and number of siblings in the population of female students at this university? Discuss this with your partner, and then write a few sentences of explanation.

5. For the population of all female students at the university, do you think it is reasonable to assume that the distribution of heights at each particular x value is approximately normal and that the standard deviation of the height distribution at each particular x value is the same? That is, do you think it is reasonable to assume that the distribution of heights for female students with zero siblings is approximately normal and that the distribution of heights for female students with one sibling is approximately normal with the same standard deviation as for female students with no siblings, and so on? Discuss this with your partner, and then write a few sentences of explanation.

6. Carry out the model utility test (H₀: β = 0). Explain why the conclusion from this test is consistent with your explanation in Step 4.

7. Would you recommend using the least-squares regression line as a way of predicting heights for women at this university? Explain.

8. After consulting with your partner, write a paragraph explaining why it is a good idea to include a model utility test (H₀: β = 0) as part of a regression analysis.

Transcribed Image Text:

Height (y) 64.2 65.4 64.6 66.1 65.1 Number of Siblings (x) 20263 Height (y) 65.5 67.2 66.4 63.3 61.7 Number of Siblings (x) 122OL 0