20200317184337stat_101a_final_exam_winter_2020_v2_new.pdf -...

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1 STAT 101A Winter 2020 Final Exam Name: ____________________________ SID: __________________________ This exam consists of Seven questions to count towards your final exam grade. Each question worth 17 points. “A Total of 102 points, Extra 2 points”. [The data size is listed below for all related questions to Housing data set] Consider the Housing data: > dim(Housing) [1] 5000 14 > ls(Housing) [1] "AGE" "BasementSize" "bathrooms" "bedrooms" [5] "bldg.full" "GarageSize" "land.acres" "main.living.area" [9] "percent.brick" "price" "rooms" "total.full" [13] "total.living.area" "year.built" Question 1. Given the following scatter plot. Call: lm(formula = price ~ bldg.full * GarageSize, data = Housing) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.700e+05 2.779e+03 61.199 <2e-16 *** bldg.full 6.265e-01 1.240e-02 50.531 <2e-16 *** GarageSizeMedium Garage -8.898e+04 6.060e+03 -14.684 <2e-16 *** GarageSizeNo Garage -1.650e+05 3.886e+03 -42.465 <2e-16 *** bldg.full:GarageSizeMedium Garage 3.886e-02 4.054e-02 0.959 0.338 bldg.full:GarageSizeNo Garage 4.801e-01 3.209e-02 14.962 <2e-16 *** --- Residual standard error: 59320 on degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on and DF, p-value: < 2.2e-16
2 > anova(m1.1) Analysis of Variance Table Response: price Df Sum Sq Mean Sq F value Pr(>F) bldg.full 1 3.4200e+13 3.4200e+13 9719.93 < 2.2e-16 *** GarageSize 2 9.4095e+12 4.7047e+12 1337.12 < 2.2e-16 *** bldg.full:GarageSize 2 7.8999e+11 3.9500e+11 112.26 < 2.2e-16 *** Residuals 4994 1.7572e+13 3.5186e+09 A) Name the response and the predictor variables listed in model m1.1 and classify them (Qualitative or Quantitative) B) Write down the MLR with its coefficients and interpret the y-intercept in model m1.1: C) Based solely on the scatter plot on page 1: Do we think the m1.1 model has three different y- intercepts? Do you think the model m1.1 has three different slopes? Explain. D) i) Write out the mathematical formula (use the values of the coefficients not the symbols) of the linear regression model for predicting price using bldg.full as a predictor for houses with Large Garage based on model m1.1. ii) Write out the mathematical formula (use the values of the coefficients not the symbols) of the linear regression model for predicting price using bldg.full as a predictor for houses with Medium Garage based on model m1.1.

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