assign 10

Stat 20 Homework 10 Please do this assignment in R Markdown and submit the knitted document.

1. Ch 10 D2: An instructor standardizes her midterm and final each semester so the class average is 50 and the SD is 10 on both tests. The correlation between the tests is around 0.50. One semester, she took all the students who scored below 30 at the midterm, and gave them special tutoring. They all scored above 50 on the final. Can this be explained by the regression effect? Answer yes or no, and explain briefly.

2. Ch 10 E2: In Pearson's study, the sons of the 72-inch fathers only averaged 71 inches in height. True or false: if you take the 71-inch sons, their fathers will average about 72 inches in height. Explain briefly.

3. Ch 10 Rev 4: In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50; both averaged 12 years of schooling completed, with an SD of 3 years.

a) Predict the educational level of a woman whose husband has completed 18 years of schooling.

b) Predict the educational level of a man whose wife has completed 15 years of schooling.

c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible?

4. Ch 11 B3: At a certain college, first-year GPAs average about 3.0, with an SD of about 0.5; the correlation with high-school GPA is about 0.6. Person A predicts first-year GPAs just using the average. Person B predicts first-year GPAs by regression, using the high-school GPAs. Which person makes the smaller r.m.s. error? Smaller by what factor?

5. Ch 11 E1: The following results were obtained for about 1000 families:

avg height of husband � 68 inches, SD � 2.7 inches;

avg height of wife � 63 inches, SD � 2.5 inches, r � 0.25

a) What percentage of the women were over 5 feet 8 inches?

b) Of the women who were married to men of height 6 feet, what percentage were over 5 feet 8 inches?

6. Ch 11 Rev 7: The freshmen at a large university are required to take a battery of aptitude tests. Students who score high on the mathematics test also tend to score high on the physics test. On both tests, the average score is 60; the SDs are the same loo. The scatter diagram is football-shaped. Of the students who scored about 75 on the mathematics test: choose one option and explain.

(i) just about half scored over 75 on the physics test.

(ii) more than half scored over 75 on the physics test.

(iii) less than half scored over 75 on the physics test.

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7. Ch 12 A3: Here are summary statistics for heights of fathers and sons:

avg height of fathers � 68 inches, SD � 2.7 inches;

avg height of sons � 69 inches, SD � 2.7 inches, r � 0.5

a) Find the regression equation for predicting the height of a son from height of father.

b) Find the regression equation for predicting the height of a father from height of son.

8. Continuing the previous problem, load the data HW10.fatherson.csv (in the Data folder under Files) and plot the points using ggplot(), including the regression line for predicting son's height from father's height, using geom_smooth() without the confidence interval (as in lecture code for 4/15 or 4/20). Also add a horizontal line through the average son's height. Verify that you get the same equation for the regression line as you did using formulas.  The data is simulated, but has the same summary statistics as above.

9. Ch 12 B1: For a large sample of men, the regression equation for predicting height from education is

predicted height = (0.25 inches per year) x (education) + 66.75 inches

Predict the height of a man with 12 years of education; with 16 years of education. Does going to college increase a man's height? Explain.

10. Ch 12 Rev 7: A statistician is doing a study on a group of undergraduates. On average, these students drink 4 beers a month, with an SD of 8. They eat 4 pizzas a month, with an SD of 4. There is some positive association between beer and pizza, and the regression equation is:

predicted number of beers = ___ x number of pizzas + 2.

However, the statistician lost the data and forgot the slope of the equation. (Perhaps he had too much beer and pizza.) Can you help him remember the slope? Explain.

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