AP Stats Linear Regression and Correlation Review

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.

An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that

• when corn prices are above average, soybean prices also tend to be above average.

• there is almost no relation between corn prices and soybean prices.

• when corn prices are above average, soybean prices tend to be below average.

• when soybean prices go up by 1 dollar, corn prices go up by 70 cents.

• the economist is confused, because correlation makes no sense in this situation.

If bivariate data set A has correlation r = 0.95, and a second bivariate data set B has correlation r = –0.95, then

• a linear model does a better job of describing the relationship between the variables in data set A than in data set B.

• a linear model does a better job of describing the relationship between the variables in data set B than in data set A.

• a linear model is the best description of the relationship between the variables in both data set A and data set B.

• you can’t tell whether either data set is best described by a linear model until you examine the scatterplots.

• a mistake has been made—r cannot be negative.

Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

• a straight line is not a good model for the data

• the correlation must be 0

• the correlation must be positive

• outliers must be present

• The regression line might or might not be a good model for the data, depending on the extent of the curve.

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 yˆ =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

• 9

• 95.5

• none of these

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 yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. 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

A least-squares regression line 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?

• 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.

Which statements below about least-squares regression are correct?

• Only I is correct.

• Only II is correct.

• Only III is correct.

• Both II and III are correct.

• All three statements—I, II, and III—are correct.

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