15 Practice: Partial Correlation and Multiple Regression and Correlation 3. The coefficient of multiple determination Suppose a researcher is trying to understand what makes living in a particular city desirable. He uses a list from a popular magazine of the current top 50 desirable cities to live in. Each city was given a desirability score by the magazine's viewers. The researcher is curious about how well he can predict those scores using only two independent variables: the median home price and the number of fast-food restaurants within 5 miles of downtown. He obtains the values for median home price and number of fast-food restaurants within 5 miles of downtown for each of the 50 cities and calculates the following values: Zero-Order Correlations: Median Home Price and # of Fast-Food Restaurants within 5 Miles of Downtown City Desirability Median # of Fast-Food Restaurants Rating Home Price within 5 Miles of Downtown City Desirability Rating 1.000 0.514 0.292 Median Home Price 1.000 0.098 # of FastFood Restaurants within 5 Miles of Downtown 1.000 The researcher computes the partial correlation of 0.283 between the city desirability rating and the number of fast-food restaurants within 5 miles of downtown controlling for the median home price. Because this value is not much different from the zeroorder correlation between the city desirability rating and the V , the researcher can consider the relationship between these two variables to be V , at least with respect to consideration of the median home price. Using the provided correlations and the given partial correlation, the coefcient of multiple determination (R2) for the multiple regression equation predicting the city desirability rating from the other two variables is V . The researcher can interpret this value to mean that V of the variance in the V is explained by The independent variable median home price predicts V of the variance in the dependent variable by itself. This suggests that also including number of fastfood restaurants within 5 miles of downtown in the regression equation V how well the equation can predict the dependent variable. The multiple correlation coefficient (R) for the multiple regression equation predicting the city desirability rating from the other two variables is V