Chapter 3 Review AP Statistics Name:

Part 1: Multiple Choice. Circle the letter for your answer.

1. Which of the following residual plots indicates a reasonable fit to a given set of data?

a) b) c) d)

e) None of these indicates a reasonable fit.

2. The graph below represents the water content in a watershed snow pack during a recent winter from

October through April. There was 200 total inches of snow with a total water content of 11 inches.

The residual plot for a least squares regression line is plotted immediately below the original plot.

Which of the following statements is true?

I) A linear regression is a good model.

II) The residual for a snowfall of 100 inches has a positive value.

III) Approximately half of the total water content for the winter had accumulated after roughly half

of the total snow for the winter fallen.

a) I only b) II only c) III only d) I and II e) I and III

3. A student computed a least squares regression line and found that the correlation coefficient was

0.83. In checking her answer she found she had switched the dependent and independent variables.

She then computed the regression line using the correct order. What is the new correlation

coefficient?

a) -1/0.83 b) -0.83 c) 0.689 d) 0.83 e) 1/.83

4. The results of a least squares linear regression are shown below:

ˆ y = 7.2 + 3.6x

x = 1.5, sx = 2

y = 12.6, sy = 8

What is the value of r2?

a) 0.12 b) 0.25 c) 0.81 d) 0.90 e) 1.23

5. A data set included the number of people per television set and the number of people per physician

for 40 countries. The Fathom screen shot below displays a scatterplot of the data with the least-

squares regression line added. In Ethiopia, there were 503 people per TV and 36,660 people per

doctor. What effect would removing this point have on the regression line?

a) Slope would increase; y-intercept would increase.

b) Slope would increase; y-intercept would decrease.

c) Slope would decrease; y-intercept would increase.

d) Slope would decrease; y-intercept would decrease.

e) Slope and y-intercept would stay the same.

Part 2: Free Response

6. The data given below show the height (in cm) at various ages (in months) for a group of children.

Age 18 19 20 21 22 23 24 25 26 27 28 29

Height 76 77.1 78.1 78.3 78.8 79.4 79.9 81.3 81.1 82.0 82.6 83.5

The equation for the least-squares regression line is predicted height = 64.94 + 0.634(age). What is

the value of the residual for the child who is 19 months old?

7. You are given the following information about a data set.

x = 8.9 sx = 3.7 r = 0.736

y = 4.7 sy = 1.2

(a) Find the equation of the least squares regression line.

(b) What is your prediction for y if x is 8.9? (Hint: You should be able to answer the question

without doing any calculations.)

8. An educator wants to determine whether students' exam scores were related to revision time. For

example, as students spent more time revising, did their exam score also increase (a positive

relationship); or did the opposite happen? To carry out the analysis, the researcher recruited 40

students. The length of time revising (in minutes) and the exam scores (points out of 100) were

recorded for all 40 participants. The Minitab output for a linear regression is shown below:

Interpret the slope and y-intercept in the context of the problem.

9. The weights of children in the Egyptian village of Nahya were recorded. Here are the mean weights

of the 170 children in that village:

Age(months) 1 2 3 4 5 6 7 8 9 10 11 12

Weight(kg) 4.3 5.1 5.7 6.3 6.8 7.1 7.2 7.2 7.2 7.2 7.5 7.8

Residual

a) Make a scatterplot of mean weight against

time. Don’t forget to scale and label your

axes appropriately.

b) What is the correlation between age and weight?

c) Determine the equation of the LSRL for

this data. Define any variables used in your

equation.

d) Plot the line on your scatterplot.

e) What is the value of r2? Interpret r2.

f) Calculate the residuals, and add them to the table

at the top of the page.

g) Use the second grid provided to construct a residual plot.

h) Use the value of r2 and the residual plot to answer this

question: Is the least squares line an acceptable summary

of the overall pattern of growth? Explain.

10. There is some evidence that drinking moderate amounts of wine helps prevent heart attacks. The

scatterplot below shows yearly wine consumption (liters of alcohol from drinking wine, per person),

and yearly deaths from heart disease (deaths per 100,000 people) in 19 developed nations.

Describe the relationship between wine consumption and deaths from heart disease.

11. Biologists studying the effects of acid rain on wildlife collected data from 163 streams in the

Adirondack Mountains. They recorded the pH (acidity) of the water and the BCI, a measure of

biological diversity. Upon creating a scatterplot of their data, they calculated the LSRL for the data,

�̂� = −66.17 + 18.91𝑥, and r2 = 0.27.

a) What is the correlation coefficient, r, for this data? Explain how you came up with this value.

b) Use the correlation coefficient to describe the relationship between these two variables.