The table for given Exercise 2 gave the average August temperature (y) and geographic latitude (x) for 20 cities in the United States. (The data are part of the temperature dataset on the companion website.) Exercise 1 gave the information that the regression equation relating these two variables is
y^ = 113.6 - 1.01x
a. The latitude at the equator is 0. Using the regression equation, estimate the average August temperature at the equator.
b. Explain why we should not use this equation to estimate average August temperature at the equator.
Exercise 1
The average August temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for given Exercise 2. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is
y^ = 113.6 - 1.01x
a. What is the slope of the line? Interpret the slope in terms of how the mean August temperature is affected by a change in latitude.
b. Estimate the mean August temperature for a city with latitude of 32.
c. San Francisco has a mean August temperature of 64, and its latitude is 38. Use the regression equation to estimate the mean August temperature in San Francisco, and then calculate the prediction error (residual) for San Francisco.
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?