HW1 LR

## lweight 0.19412839 1.000000000 0.3075247 0.43493174 0.10877818 0.10023889 ## age 0.22499988 0.307524741 1.0000000 0.35018592 0.11765804 0.12766778 ## lbph 0.02734971 0.434931744 0.3501859 1.00000000 -0.08584327 - 0.00699944 ## svi 0.53884500 0.108778185 0.1176580 -0.08584327 1.00000000 0.67311122 ## lcp 0.67531058 0.100238891 0.1276678 -0.00699944 0.67311122 1.00000000 ## gleason 0.43241705 -0.001283003 0.2688916 0.07782044 0.32041222 0.51482991 ## pgg45 0.43365224 0.050846195 0.2761124 0.07846000 0.45764762 0.63152807 ## lpsa 0.73446028 0.354121818 0.1695929 0.17980950 0.56621818 0.54881316 ## gleason pgg45 lpsa ## lcavol 0.432417052 0.4336522 0.7344603 ## lweight -0.001283003 0.0508462 0.3541218 ## age 0.268891599 0.2761124 0.1695929 ## lbph 0.077820444 0.0784600 0.1798095 ## svi 0.320412221 0.4576476 0.5662182 ## lcp 0.514829912 0.6315281 0.5488132 ## gleason 1.000000000 0.7519045 0.3689867 ## pgg45 0.751904512 1.0000000 0.4223157 ## lpsa 0.368986693 0.4223157 1.0000000 Which pair of variables has the highest R 2 (exclude any correlation between a variable and itself)? Hint: You can find the highest R 2 manually or using R statements # Enter your code below diag (corr_var) <- 0 highcorr <- max (corr_var) indices <- which (corr_var == highcorr, arr.ind = TRUE ) var1 <- rownames (corr_var)[indices[ 1 , 1 ]] var2 <- colnames (corr_var)[indices[ 1 , 2 ]] cat ( "Pair of variables with the highest R^2 (excluding self- correlation): \n " ) ## Pair of variables with the highest R^2 (excluding self- correlation): cat (var1, "and" , var2, "with R^2 =" , highcorr) ## pgg45 and gleason with R^2 = 0.7519045 Pair of variables with the highest R^2 (excluding self-correlation):pgg45 and gleason with R^2 = 0.7519045

m8 <- lm (lpsa ~ lcavol + svi + lcp + pgg45 + gleason + lweight + lbph + age, data = prostate) Question 6: Extract the residual standard error (RSE) and R 2 for each model and put these values into a table. The table should have three columns: The model number (1 to 8), RSE, and R 2 . Create two plots. The x-axis should show the model number in both plots. The y-axis should show the RSE in the first plot and R 2 in the second. # creating a data frame to store the RSE and correlation of each regression # The frame will have a row for each regression. The regression will be numbered from 1 to 8 regDf <- data.frame ( RegNo = 1 : 8 ) # adding two columns for storing the errors and correlations: regDf $ rse <- NA regDf $ rsq <- NA # Enter your code below regDf <- data.frame ( RegNo = 1 : 8 ) regDf $ rse <- sapply ( 1 : 8 , function (i) summary ( get ( paste0 ( "m" , i))) $ sigma) regDf $ rsq <- sapply ( 1 : 8 , function (i) summary ( get ( paste0 ( "m" , i))) $ r.squared) print (regDf) ## RegNo rse rsq ## 1 1 0.7874994 0.5394319 ## 2 2 0.7556684 0.5803761 ## 3 3 0.7587017 0.5815006 ## 4 4 0.7568200 0.5880516 ## 5 5 0.7609184 0.5881043 ## 6 6 0.7208619 0.6343914 ## 7 7 0.7166818 0.6426346 ## 8 8 0.7084155 0.6547541 Creating the plots: par ( mfrow = c ( 1 , 2 )) # Enter your code below par ( mfrow = c ( 1 , 2 )) plot (regDf $ RegNo, regDf $ rse, type = "b" , xlab = "Model Number" , ylab = "Residual Standard Error" , main = "RSE vs Model Number" )

plot (m5)