12. Regression

Bear Markets Explain why it does not make sense to find a least-squares regression line for the Bear Market data from Problem 34 in Section 4.1.  

Explain the meaning of Legendre’s quote given.

Explain what each point on the least-squares regression line represents.

The _____ _____ _____, R^2, quantifies the proportion of total variation in the response variable explained by the least-squares regression line.

What is the simple least-squares regression model? What are the requirements to perform inference on a simple least-squares regression line? How do we verify that these requirements are met?

[DATA] Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following table lists the temperature (in degrees Fahrenheit, °F) and the number of chirps per second for the striped ground cricket.

i. Construct a 90% prediction interval for the number of chirps found in part (h).

[DATA] The following data represent the height (inches) of boys between the ages of 2 and 10 years.

h. Explain why the predicted heights found in parts (a) and (f) are the same, yet the intervals are different.

[DATA] Concrete As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete:

d. Assuming the residuals are normally distributed, test whether a linear relation exists between 7-day strength and 28-day strength at the alpha = 0.05 level of significance

Regression and Predictions

Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1.

Find the regression equation, letting the first variable be the predictor (x) variable.

Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5.

Powerball Jackpots and Tickets Sold Listed below are the same data from Table 10-1 in the Chapter Problem, but an additional pair of values has been added from actual Powerball results. (Jackpot amounts are in millions of dollars, ticket sales are in millions.) Find the best predicted number of tickets sold when the jackpot was actually 345 million dollars. How does the result compare to the value of 55 million tickets that were actually sold?

Regression and Predictions

Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1.

Find the regression equation, letting the first variable be the predictor (x) variable.

Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5.

Taxis Use the distance/fare data from Exercise 15 and find the best predicted fare amount for a distance of 3.10 miles. How does the result compare to the actual fare of \$15.30?