The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 2. The regression equation for these data was given in Exercise 1 as = 1.26 - 2.34x. The value of r2 for this relationship is 73.3%. What is the correlation between average January temperature and latitude for these 20 cities?
Exercise 1
The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 2. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is
y^ = 1.26 - 2.34x
a. What is the slope of the line? Interpret the slope in terms of how mean January temperature is related to change in latitude.
b. 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 2.
c. Predict the average January temperature for a city with latitude 33.
d. Refer to part (c). Identify the two cities in the table that have a 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.
Exercise 2
The data in the following table are the geographic latitudes and the average August and January temperatures (Fahrenheit) for 20 cities in the United States. The cities are listed in geographic order from south to north. (These data are part of the temperature dataset on the companion website.)
a. Draw a scatterplot of y = August temperature versus x = latitude.
b. Is the pattern linear or curvilinear? What is the direction of the association?
c. Are there any cities that appear to be outliers because they don't fit the pattern of the rest of the data? If so, which city or cities are they?