In a Study of Housing Demand, the County Assessor Is Interested

In a study of housing demand, the county assessor is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor feels that the most important variable affecting selling price (measured in thousands of dollars) is the size of house (measured in hundreds of square feet). He randomly selected 15 houses and measured both the selling price and size, as shown in the following table.

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.:.

a. Plot the data.

b. Determine the estimated regression line. Give an economic interpretation of the estimated slope (b) coefficient.

c. Determine if size is a statistically significant variable in estimating selling price.

d. Calculate the coefficient of determination.

e. Perform an F-test of the overall significance of the results.

f. Construct an approximate 95 percent prediction interval for the selling price of a house having an area (size) of 15 (hundred) square feet.

SOLUTION:

This is a housing problem with Price in thousands and Size in 100 square feet increments. The Excel output is:

| |Coefficients |Standard Error |t Stat |

|Intercept |206.28 |9.80 |21.06 |

|Size |3.96 |0.40 |9.99 |

a. Plotting the data, the intercept is 206.28 and rises by 3.96 for each 100 square feet.

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b. If a 10x10 foot room is a quite small bedroom, each room adds about $4,000 dollars to the price.

c. The t-value is 9.99, which is greater than critical t-statistic of 2.16037 with 13 degrees of freedom, so this is statistically different than zero.

d. The coefficient of determination is the R-square, which is .88.

|Regression Statistics |

|Multiple R | 0.94 |

|R Square | 0.88 |

|Adjusted R...