The study of U.S. cities in Exercise R2.29 found the mean January Temperature (degrees Fahrenheit), Altitude (feet above sea level), and Latitude (degrees north of the equator) for 55 cities. Here’s the correlation matrix:

a) Which seems to be more useful in predicting January Temperature: Altitude or Latitude? Explain.
b) If the Temperature were measured in degrees Celsius, what would be the correlation between Temperature and Latitude?
c) If the Temperature were measured in degrees Celsius and the Altitude in meters, what would be the correlation?
d) What would you predict about the January Temperature in a city whose Altitude is two standard deviations higher than the average Altitude?

Data From Review Exercise 2.29

Data from 50 large U.S. cities show the mean January Temperature and the Latitude. Describe what you see in the scatterplot.

Jan. Temp Latitude Altitude Jan. Temp Latitude Altitude 1.000 -0.848 -0.369 1.000 0.184 1.000