Problem#4 [22 points]: Suppose simple linear regression is fitted to the data {(x1, y1), ... (X23, Y23)), with E(Y | X = x) = Pot Bix, Var(Y | X =x) =0' The coefficient table and ANOVA table below shows some of the estimated values: Coefficient Table ANOVA Table Estimate Std. Error T-statistic p-value of SS MS F-statistic p-value Intercept 0.2865 -1.584 Regression 0.7713 X -0.0996 -1.852 Residuals Total (a) [11 points] Replicate the two tables above, and fill in ALL the missing values (in 5 significant figures) from the two tables. (The p-values can be obtained from R commands like "> 1-pf(Fo, df1, df2)" for the right-hand tailed probability of Fan, ap or "pt(tad)" for the cdf of ta) (b) [3 points] Based on the results in part (a), what is the sample correlation coefficient between x and y? That is, r, - Corr(x,y)-E(x; -D)(1 -D)/VZ(x;-x)'E(;-D)'. (c) [8 points] Based on the results in part (a), test the hypotheses on whether Bo = 0.2 at a = 0.05. You should setup the 4 steps of hypothesis testing as on Ch2 page 66. Problem#5 (R problem) [20 points]: The R library 'alr4' contains the "segreg" data, which contains the electricity consumption (in KWH) and mean temperature (in F) for a building at the University of Minnesota Twin Cities campus for 39 months in 1988-1992. (https://rdrr.io/cran/alr4/man/segreg.html) Suppose that we are interested in how the electricity consumption (y=segreg$C) is affected by the monthly mean temperature (x=segreg$Temp), primarily driven by the use of air conditioning. (a) [10 points] Based on the R codes similar to those from Ch2 page 23, obtain (i) the OLS estimates Bo , B, and o2 , and (ii) RSS. (b) [6 points] Based on the plot and the abline functions as in Ch1 page 26, generate the scatterplot of the data, and add the regression line obtained in part (a) to the plot. (c) [4 points] Suppose an outlier is defined as observation (x;, y:) with le, > 20 . Do you think there is outlier in the data set? Verify. (Note: A more precise definition of outlier will be introduced in Chapter 7, which removes the impact of the outlier (x; y;) itself when estimating o). End of the Assignment- Page 2/2