AP Stats Linear Regression and Correlation Review

Other things being equal, larger automobile engines are less fuel efficient. You are planning an experiment to study the effect of engine size (in liters) on the fuel efficiency (in mpg) of sport utility vehicles. In this study

• gas mileage is a response variable, and you expect to find a negative association.

• gas mileage is a response variable, and you expect to find a positive association.

• gas mileage is an explanatory variable, and you expect to find a strong negative association.

• gas mileage is an explanatory variable, and you expect to find a strong positive association.

• gas mileage is an explanatory variable, and you expect to find very little association.

In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was  ŷ = 10 + 0.9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

• 85.5

• 90

• 95

• 95.5

• none of these

In the course described in #2, Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?

• -2.0

• 2.0

• 3.0

• 93

• none of these

The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs

(one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

• much smaller than 0.52

• slightly smaller than 0.52

• unchanged: equal to 0.52

• slightly larger than 0.52

• much larger than 0.52

Which statements below about least-squares regression are correct?

I. Switching the explanatory and response variables will not change the least-squares regression line.

II. The slope of the line is very sensitive to outliers in the x direction with large residuals.

III. A value of r^2 close to 1 does not guarantee that the relationship between the variables is linear.

• Only I

• Only II

• Only III

• Both II and III

• I, II, and III

A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is ŷ = 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating.

Which of the following statements must be true?

• For each one-point increase in performance rating, the raise will increase on average by$1400.

• The actual relationship between salary raises and performance rating is linear.

• The residuals for half the observations in the dataset will be positive.

• The correlation between salary raise and performance rating is negative.

• If the mean performance rating is 1.2, then the mean raise is $3800.

For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by ŷ = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months).

Joseph is 22.5 months old. What is his predicted height?

• 50.8

• 64.96

• 65.96

• 79.11

• 87.4

For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by ŷ = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months).

Loretta is 20 months old and is 80 cm tall . What is her residual?

• -2.47

• 2.47

• -12.6

• 12.6

• 77.53

A LSRL for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model? (click on the picture to enlarge)

• A residual plot is not an appropriate means for evaluating a linear model.

• The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players.

• The curved pattern in the residual plot suggests that the linear model is not appropriate.

• There are not enough data points to draw any conclusions from the residual plot.

• The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.

A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be –1.08. On the basis of this you would tell the college that

• the entrance exam is a good predictor of success

• the exam is a poor predictor of success

• students who do best on this exam will be poor students

• students at this school are underachieving

• the college should hire a new statistician (like Mrs. Frias)