A recent study looked at square footage as the predictor of a house’s selling pr
ID: 3160458 • Letter: A
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]