Question

A random sample of records of sales of homes from the files maintained by a board of realtors in a particular city gives the Price and Size​ (in square​ feet) of 117 homes. They hope to predict Price​ (in thousands of​ dollars) from Size. The correlation is

r=0.920.
What would one predict about the Price of a home 1 standard deviation above average in​ Size? Select the correct choice below and fill in the answer box to complete your choice.

A.Price should be nothing times the mean price.
B.Price should be nothing standard​ deviation(s) times the mean price.
C.Price should be nothing above the mean in price.
D.Price should be nothing standard​ deviation(s) above the mean in price.

Answer 1

Given a high correlation coefficient of 0.920, a home that is one standard deviation above average in size is expected to also have a higher price.

Step-by-step explanation:

The correlation coefficient, r, is a measure of the linear relationship between two variables. In this case, it is 0.920, which indicates a strong positive relationship between the Size of homes (independent variable) and their Price (dependent variable). When a home is one standard deviation above the average Size, its Price is also expected to be higher. However, to precisely predict how much above the mean price the home would be, we would need the regression equation and the values for standard deviations of both Price and Size. Without these values, we can only qualitatively predict that the home's price will be higher due to the high correlation.