The accompanying table shows a portion of a data set that refers to the size of

Question

The accompanying table shows a portion of a data set that refers to the size of a home (in square feet) and its property taxes owed by the owner (in $) in an affluent suburb 30 miles outside New York City. PictureClick here for the Excel Data File Size (in square feet) Property Taxes (in $) 2,352 21,987 2,362 17,343 1,776 18,279 1,118 15,645 5,712 43,954 2,592 33,653 2,134 15,105 1,905 16,749 2,024 18,239 1,389 16,048 1,381 15,135 3,028 36,016 2,771 31,083 3,374 42,000 1,556 14,370 3,971 38,953 3,934 25,373 2,321 22,971 3,557 16,169 2,878 29,272 a. Determine the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.) 111formula11.mml = + Size. b. Interpret the slope coefficient. As Size increases by 1 square foot, the property taxes are predicted to increase by $6.91. As Property Taxes increase by 1 dollar, the size of the house increases by 6.91 ft. c. Predict the property taxes for a 1,200-square-foot home. (Round your answer to 2 decimal places.) 111formula11.mml rev: 12_20_2016_QC_CS-72935 eBook & Resources eBook: Estimate the simple linear regression model and interpret the coefficients.

Explanation / Answer

Following is the output of regression analysis generated by excel:

The regression equation is

Taxes = 6398.22 + 6.91* Property

(b)

Slope is: 6.91

As Size increases by 1 square foot, the property taxes are predicted to increase by $6.91.

(c)

For X = 1200, predicted taxes is

Taxes = 6398.22 + 6.91* 1200 = $14,690.22

SUMMARY OUTPUT Regression Statistics Multiple R 0.770981234 R Square 0.594412063 Adjusted R Square 0.571879399 Standard Error 6495.429069 Observations 20 ANOVA df SS MS F Significance F Regression 1 1112988759 1112988759 26.38001808 6.92109E-05 Residual 18 759430778.2 42190598.79 Total 19 1872419537 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 6398.217216 3797.034665 1.685056309 0.109236111 -1579.056585 14375.49102 Property,X 6.912432256 1.345839726 5.136148176 6.92109E-05 4.084927917 9.739936596

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