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## Problem 3 A real estate broker constructed a multiple linear regressionmodel for house prices in his

Problem 3 A real estate broker constructed a multiple linear regressionmodel for house prices in his area using as explanatory variables size of ahouse, age of a house, lotsize and source of energy used to heat a house. Heintroduced the following variables:Price, sale price of a house (in \$1000)Size, size of a house (in 100 sq ft)Age, age of a house (in years)Lotsize, size of a lot (in 1000 sq ft)There are three sources of energy: electricity, heating oil and natural gas.He coded this information as followsGas = 1 if a house is heated by natural gas= 0 if notOil = 1 if a house is heated by heating oil= 0 if notAnswer the questions below with the help of Minitab outputa) Is the coe?cient of Oil statistically significant at = 001? (State 0and 1 test statistic and your conclusion). Interpret the coe?cient of Oil.b) Which two explanatory variables are most highly correlated with eachother?c) What proportion of sample variation in Price is explained by thesimple regression model of Price on Age?d) How do you explain the lack of the statistical significance of Agein the multiple regression in view of Age being statistically significant at = 005 in the simple regression of Price on Age?e) A real estate broker chose a three-variable model as the final modelfor Price. Why did she make this choice? Interpret the coe?cient of Oil inthis model.f ) Using the final model, construct the confidence interval for the expected sale price of 1800 sq ft houses, which are heated by the electricity,and have lotsizes of 14,000 sq ft. The SEfit for these values of predictors is8149.95.3 Minitab Output for Problem 3Price = – 5.5 + 4.14 hsize – 10.8 oil + 2.67 gas + 0.143 age + 3.14 lotsizePredictorConstanthsizeoilgasagelotsize Coef-5.514.1435-10.7912.6690.14303.1369 S = 4.71154 SE Coef13.670.51703.0694.2290.61050.9439 R-Sq = 96.8% T-0.408.01 P0.6960.000 0.630.233.32 0.5440.8200.009 R-Sq(adj) = 95.0% Analysis of VarianceSourceRegressionResidual ErrorTotal DF5914 SS6030.4199.86230.2 MS1206.122.2 F54.33 P0.000 Correlations: Price, hsize, oil, gas, age, lotsizePrice0.8050.000 hsize oil -0.5220.046 -0.0990.725 gas 0.4860.066 0.0350.903 -0.5000.058 age -0.5210.046 -0.8090.000 0.0240.932 0.1700.546 0.3720.172 -0.1710.542 -0.4490.093 0.7600.001 hsize lotsize oil gas age 0.4100.129 Best Subsets Regression: Price versus hsize, oil, gas, age, lotsizeResponse is Price Vars12345 R-Sq64.891.696.696.896.8 R-Sq(adj)62.090.195.795.595.0 MallowsCp87.914.72.44.16.0 S12.9976.62204.36694.48344.7115 lotso g a ii a g zl s e e hsizeXXX XX X XX X X X XXXX Regression Analysis: Price versus hsize, oil, lotsizeThe regression equation isPrice = – 5.33 + 4.09 hsize – 11.1 oil + 3.61 lotsize