For the real estate data of the previous exercise, consider the value of the number of bedrooms in modeling the price of a home. The correlation between Price and Bedrooms is 0.116. Here is a regression model:

a) What is a correct interpretation of the coefficient of Bedrooms?
b) The correlation of Price and Bedrooms is positive. How can the regression coefficient of Bedrooms be negative?
Here is a partial regression plot for the coefficient of Bedrooms along with a least squares regression line:

c) What is the slope of the regression line in the partial regression plot?
d) A homeowner proposes to convert his living room to a bedroom, thinking that more bedrooms would make his home more valuable. What do you think?

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Response variable is: Price R squared = 14.6% s = 266899 Variable Intercept Living area Bedrooms Coefficient 308100 135.089 -43346.8