Consider the Housing data dim(Housing) 1 3000 13 names (Housing) 1 logprice 4 land acres 7 bathrooms 10 Bricks 13 AGE bldg full main living area bedrooms total full total living area I 'rooms Garage BasementSize Question 1 Given the following scatter plot House Price Vs Total Full logprice 17 5 15 0 12 5 10 0 7 5 5 0 0e 00 5e 05 1e 06 total full m1 1 summary(m1 1) factor(Garage) No Yes Garage No Yes 1 Call 1m (formula logprice total full Garage, data Coefficients Housing) Estimate Std Error t value Pr( t ) (Intercept) total full GarageYes total full GarageYes 7 639e 06 Residual standard error 0 5249 on degrees of freedom Multiple R squared ' Adjusted R squared 1 027e 01 3 1360 02 327 69 2e 16 9 336e 06 2 669e 07 34 98 2e 16 1 619e 00 4 007e 02 40 42 2e 16 2 878e 07 26 54 2e 16 F statistic anova (m1 1) and on DF, p value 2 2e 16 Analysis of Variance Table Response logprice total full Garage total full Garage Residuals Df Sum Sq Mean Sq F value Pr( F) 1 582 21 582 21 2112 81 2 2e 16 1 317 30 1 194 07 2996 825 58 317 30 1151 46 2 2e 16 194 07 704 26 2 2e 16 0 28 A) Name the response and the predictor variables listed in model m1 1 and classify them (as Qualitative or Quantitative) B) Write down the MLR with its coefficients values and interpret each of the coefficients in model m1 1 C) Based solely on the scatter plot on page 1 Do you think that m1 1 model has two different y intercepts based on the house Garage status Do you think the model m1 1 has two different slopes based on the house Garage status Explain D) i) Write down the mathematical formula (use the actual values of the coefficients not beta symbols) of the linear regression model for predicting houses logprice using total full as a numerical predictor for No Garage houses only based on model m1 1 ii) Write down the formula (use the values of the coefficients not beta symbols) of the linear regression model for predicting houses logprice using total full as a numerical predictor for Yes Garage houses only based on model m1 1 E) Calculate residual degrees of freedom, F statistic, R and Adjusted R based on model m1 1

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Question: Consider the Housing data: > dim(Housing) [1] 3000 13 > names (Housing) [1] logprice [4] land.acres [7] bathrooms [10] Bricks [13] AGE bldg.full main.living.area

Consider the Housing data: > dim(Housing) [1] 3000 13 > names (Housing) [1] "logprice" [4] "land.acres" [7] "bathrooms" [10] "Bricks" [13] "AGE" "bldg.full" "main.living.area" "bedrooms" "total.full" "total.living.area" "I 'rooms" "Garage" "BasementSize" Question 1. Given the following scatter plot. House Price Vs. Total Full logprice 17.5- 15.0- 12.5- 10.0- 7.5- 5.0- 0e+00 5e+05 1e+06 total.full > m1.1 summary(m1.1) factor(Garage) No Yes Garage No Yes 1 Call: ~ 1m (formula = logprice total.full* Garage, data Coefficients: = Housing) Estimate Std. Error t value Pr(>|t|) (Intercept) total.full GarageYes total.full:GarageYes -7.639e-06 Residual standard error: 0.5249 on degrees of freedom Multiple R-squared: ' Adjusted R-squared: 1.027e+01 3.1360-02 327.69

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