A recent study looked at square footage as the predictor of a house’s selling pr

Question

A recent study looked at square footage as the predictor of a house’s selling price. Listed below is a random sample of 5 houses sold within the last year. Square footage and Selling Price are listed in thousands. Square Footage Selling Price 4.20 485 3.60 325 3.20 295 3.50 305 3.80 365 Sum: 18.30 1775 Using sales price as the dependent variable and square footage as the independent variable complete the following: a. Determine the correlation coefficient. b. Interpret the correlation coefficient. c. Determine the regression equation. d. For a house with 4000 square feet (use 4.0 in your equation), determine the expected selling price. e. Calculate and interpret the coefficient of determination.

Explanation / Answer

a)

Using technology, we get the correlation,              
              
r =    0.947002964   [ANSWER]

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b)

As r is close to +1, We see a strong positive linear relationship between square footage and selling price.

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c)

Using technology, we get              
              
slope =    197.4637681          
intercept =    -367.7173913          
              
Thus, the regression line is              
              
Price^ =    197.4637681*Foot - 367.7173913 [ANSWER]

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d)

Thus, if Foot =    4
  
Then  
  
Price^ =    422.1376812 thousand dollars [ANSWER]

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e)

Thus, the coefficient of determination is  
  
r^2 =    0.896814614

Hence, around 89.68% of variation in selling price is explained by the variation in square footage. [ANSWER]

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