Chapter 3, Problem 3.24E

The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 3.9. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is

$\stackrel{⌢}{y}=126-2.34$

1. What is the slope of the line? Interpret the slope in terms of how mean January temperature is related to change in latitude.
2. Pittsburgh, Pennsylvania, has a latitude of 40, and Boston, Massachusetts has a latitude of 42. Use the slope to predict the difference in expected average January temperatures for these two cities Compare your answer to the actual difference in average January temperature for these two cities using the data shown in the table for Exercise 3.9.
3. Predict the average January temperature for a city with latitude 33.
4. Refer to part (c). Identify the two cities in the table that have latitude of 33 and compute the residual (prediction error) for each of these cities. Discuss the meaning of these two residuals in the context of this example, identifying whether each city is warmer or cooler than predicted.