Exercise 4.Mary is investigating the determinants of house prices in 90 cities. She gathers information on housevalue in log (Inhseval), the size of the house (sizehse), and income per capita in log (Inincome). Shealso gathers information on the property tax rate, specifically if cities have the low property tax rate(less than 2.5%), or the high property tax rate (2.5% or more). She runs the following regression:Ln(hseval;)= a + B₁(sizehse;) + B2 (income)+ &;And then she separates the regression by low and high property tax rate.The results of her regression analysis are given in the tables below.Regression results: Dependent variable is Ln(hseval;)SourceModelResidualTotal1nhseval.sizehseInincomeconsSourceModelResidual-> lowtax High tax rateTotal1nhsevalsizehseinincome_consSourceModelResidualTotalSS1nhseval1.560645712.980392144.54103785sizehseinincome_consSS-> lowtax Low tax rateCoef. Std. Err..4007332 .088795.6444489 .2287038-4.40504 1.722207.6748285411.062477991.73730653Coef..3822666.5161721-3.326388SS.8615302131.477051842.33858205dfCoef.28789 .051022897df24648Std. Err..0959503.2452281.87827df238MSStd. Err..780322856.034257381.4760923 .1477824.5609946 .388544-4.064405 2.855013tMS4.51 0.0002.82 0.006-2.56 0.012.33741427.023097348.036193886tP>ItlMSNumber of obs =F(2, 87)Prob > F=R-squaredAdj R-squared =Root MSE=40 .058464551.430765107.038869785t3.98 0.0002.10 0.041-1.770.083P>|t|Number of obsF (2, 46)Prob> FR-squaredAdj R-squaredRoot MSE[95% Conf. Interval]P>|t|.2242435 .5772228.18987541.099022-7.828113-.98196723.22 0.0031.44 0.157-1.42 0.163Number of obsF (2, 38)Prob > FR-squaredAdj R-squaredRoot MSE9022.780.00000.34370.3286.18509.1891286.0225536-7.107151[95% Conf. Intervall.57540461.009791.45437394914.610.00000.38840.3618.15198.1769225-.2255716-9.8440764111.080.00020.36840.3352.19715[958 Conf. Intervall.77526211.3475611.715266a. What can Mary conclude about the significance and the effect of the coefficients in the aboveregressions, and how do they change when separating across property tax rates? Carefully explain theeffect of the independent variables in the three regressions presented.b. What is the meaning of the R squared, and how does it change?

Solution: From the given information, the dependent variable is house value. Independent variables…

Mary is investigating the determinants of house prices in 90 cities. She gathers information on house value in log (Inhseval), the size of the house (sizehse), and income per capita in log (Inincome). She also gathers information on the property tax rate, specifically if cities have the low property tax rate (less than 2.5%), or the high property tax rate (2.5% or more). She runs the following regression: Ln(hseval;)= a + B₁(sizehse;) + B2 (income)+ & And then she separates the regression by low and high property tax rate. The results of her regression analysis are given in the tables below. Regression results: Dependent variable is Ln(hseval;) Source Model Residual Total 1nhseval sizehse Inincome cons Source Model Residual Total -> lowtax = High tax rate 1nhseval sizehse Inincome cons Source Model Residual Total SS 1nhseval 1.56064571 2.98039214 sizehse Inincome cons 4.54103785 SS -> lowtax Low tax rate Coef. Std. Err. .4007332 .088795 .6444489 .2287038 -4.40504 1.722207 .674828541 1.06247799 1.73730653 .3822666 .5161721 -3.326388 df SS 861530213 1.47705184 2.33858205 2 87 .780322856 .034257381 89 .051022897 Coef. Std. Err. df 2 46 .0959503 .245228 1.87827 df 2 38 MS 48 .036193886 40 Coef. Std. Err. t P>Itl MS 4.51 0.000 2.82 0.006 .1898754 -2.56 0.012 -7.828113 .33741427 .023097348 t MS Number of obs F(2, 87) Prob> F R-squared Adj R-squared Root MSE .430765107 .038869785 .058464551 3.98 0.000 2.10 0.041 -1.77 0.083 t Number of obs E (2, 46) Prob> F R-squared P> It| Adj R-squared Root MSE [95% Conf. Interval] .2242435 .5772228 1.099022 -.9819672 P>It| Number of obs F (2, 38) Prob > F R-squared 4760923 -1477824 3.22 0.003 .5609946 .388544 1.44 0.157 -4.064405 2.855013 -1.42 0.163 .1891286 .0225536 -7.107151 Adj R-squared Root MSE = 90 22.78 0.0000 0.3437 0.3286 .18509 [95% Conf. Intervall .1769225 -.2255716 -9.844076 49 14.61 0.0000 0.3884 0.3618 .15198 .5754046 1.009791 .4543739 41 11.08 0.0002 0.3684 0.3352 .19715 [95% Conf. Intervall .7752621 1.347561 1.715266 a. What can Mary conclude about the significance and the effect of the coefficients in the above regressions, and how do they change when separating across property tax rates? Carefully explain the effect of the independent variables in the three regressions presented. b. What is the meaning of the R squared, and how does it change?