AP Stats Linear Regression and Correlation Review

Which of the following statements is not true of the correlation r between the lengths in inches and weights in pounds of a sample of brook trout?

• r must take a value between -1 and 1.

• r is measured in inches.

• If longer trout tend to also be heavier, then r>0.

• r would not change if we measured the lengths of the trout in centimeters instead of inches.

Write the linear regression equation for the data set foot length (x) and height (y).

• yhat = 28.93 + 1.155x
• height = 28.39(foot length) + 1.155
• yhat = 1.878 + 117.99x
• height = 117.99 + 1.878(foot length)

In order to linearize data that is growing exponentially, you must take:

• Log of x

• Log of y

• Log of y-hat

• Log of x and y

What does r² stand for?

• correlation coefficient
• coefficient of determination
• slope of the line of best fit (LOBF) for a sample
• slope of the line of best fit (LOBF) for a population

Which is TRUE?
I.  Random scatter in the residuals indicates a linear model.
II.  If two variables are very strongly associated, then the correlation between them will be near 1 or -1.
III.  Changing the units of measurement for x or y changes the correlation coefficient.

• I only
• II only
• I and II only
• I, II and III

How do you calculate a residual?

• Observed - Predicted
• Predicted - Observed

After performing analyses on a set of data, Mr. Trejo examined the scatter plot of the residual values for each analysis. Which scatter plot indicated the best linear fit for the data?

• A

• B

• C

Predicting the temperature for a heating time of 70 minutes is an example of what?

• Interpolation

• Outlier Rule

• Residual

• Extrapolation

A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds’ total length, in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?

• Underestimate, because the residual is positive.

• Underestimate, because the residual is negative.

• Overestimate, because the residual is positive.

• Overestimate, because the residual is negative.

• Neither, because the residual is 0.

The equation of the least squares regression line for a set of data is y=0.68+1.21x. What is the residual for the point (3, 4)?

• -0.31

• -0.68

• -1.52

• -3.63

• -4.31