A1: Compute the coefficient of determination based on the above regression repor

Question

A1: Compute the coefficient of determination based on the above regression report:

A2: Predict the market price of a home with 1200 square feet, 1 car garage, 2 bedrooms.

A3: Predict the market price of a home with 2500 square feet, 2 car garages, 3 bedrooms:

ANOVA MS Significance F Regression Residual Total 3 6915.163752 2305.054584 38.25859023 0.000103625 7 421.7453385 60.24933407 10 7336.909091 t Stat P-value Lower 95% 95% Intercept Sq Ft Garage Bedrooms Coefficients Standard Error 26.44037042 11.52795953 2.293586333 0.055513321 -0.818922254 53.69966309 30.80340383 14.65878551 2.101361249 0.073722865 3.859115886 65.46592354 12.56745088 4.459141057 2.818356881 0.025834115 2.023257797 23.11164397 4.575960456 7.143016784 0.640620146 0.54216428 -12.31459026 21.46651117 1 RESIDUAL OUTPUT 0 3 Observation edicted (in $1000 Residuals 1 66.39569516 -1.395695157 2 69.47603554 3.52396446 3 83.58365661 1.416343386 4 83.29301714 3.706982856 5 105.1014892 -7.101489175 6 98.69471906 -3.694719059 7 134.566262 -9.566262045 112.75779 -7.757790014 9 115.8381304 9.161869603 134.566262 2.433737955 11 140.7269428 9.273057189 2 10

Explanation / Answer

A1) Coefficient of determination(R2) is the explained part of the model by the regression equation.

R2 = (Regression SS/Total SS)*100 = (6915.163752/7336.909091)*100 = 94.25%

A2) To determine the dependent variable i.e Market Price, the regression equation needs to be in place. Below is the regression equation based on the coefficents from the report -

Y(Market Price) = c1X1+c2X2+c3X3+b where c1,c2,c3 are coefficients of Sq.Ft, Garage and Bedrooms respectively and b is the intercept valeu.

Y = 30.8X1+12.57X2+4.58X3+26.44

Y = (30.8*1200)+(12.57*1)+(4.58*2)+26.44 = 37008 $

Hence, market price = 37008 $(approx)

A3) Y = 30.8X1+12.57X2+4.58X3+26.44

Y = (30.8*2500)+(12.57*2)+(4.58*3)+26.44 = 77066 $(approx)

Hence, market price = 77066 $(approx)

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