# EBook Problems GLM Regress

## EBook Problems Set - Regression

### Problem 1

Use the information from the Heights of Fathers and Sons to write the linear model that best predicts the height of the son from the height of the father.

- Choose one answer.

*(a) Son's height = 35 + 0.5*Father's height'*

*(b) Son's height = 1.00 + 1.00* Father's height*

*(c) The model cannot be determined without the actual data*

*(d) Son's height = 0.5 + 35*Father's height*

### Problem 2

A congressional report investigates the relationship between income of parents and educational attainment of their daughters. Data are from a sample of families with daughters age 18-24. Average parental income is $29,300, average educational attainment of the daughters is 13.1 years of schooling completed, and the correlation is 0.37.

The regression line for predicting daughter’s education from parental income is reported as: Predicted education = 0.000617*(income) + 8.1

Is the following statement true or false? "The above line is the regression line to predict education from income."

*(a)True.*

*(b)False.*

### Problem 3

In the early 1900's when Francis Galton and Karl Pearson measured 1078 pairs of fathers and their grown-up sons, they calculated that the mean height for fathers was about 68 inches with deviation of 3 inches. For their sons, the mean height was 69 inches with deviation of 3 inches. (The actual numbers are slightly smaller, but we will work with these values to keep the calculations simple.) The correlation coefficient was 0.50. Use the information to calculate the slope of the linear model that predicts the height of the son from the height of the father.

- Choose one answer.

*(a) 0.50*

*(b) The slope cannot be determined without the actual data*

*(c) 35.00*

*(d) 3/3 = 1.00*

### Problem 4

Suppose that wildlife researchers monitor the local alligator population by taking aerial photograhs on a regular schedule. They determine that the best fitting linear model to predict weight in pounds from the length of the gators inches is:

Weight = -393 + 5.9*Length with r2 = 0.836.

Which of the following statements is true?

- Choose one answer.

*(a) A gator that is about 10 inches above average in length is about 59 pounds above the average weight of these gators.*

*(b) The correlation between a gator's length and weight is 0.836.*

*(c) The correlation between a gator's height and weight cannot be determined without the actual data.*

*(d) The correlation between a gator's height and weigth is about -0.914.*

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