#LESSON 5 SIMPLE LINEAR REGRESSION (27/04/2021) library(ISwR) data(thuesen) attach(thuesen) thuesen ### blood.glucose short.velocity #1 15.3 1.76 #2 10.8 1.34 #3 8.1 1.27 #4 19.5 1.47 #5 7.2 1.27 #6 5.3 1.49 #7 9.3 1.31 #8 11.1 1.09 #9 7.5 1.18 #10 12.2 1.22 #11 6.7 1.25 #12 5.2 1.19 #13 19.0 1.95 #14 15.1 1.28 #15 6.7 1.52 #16 8.6 NA #17 4.2 1.12 #18 10.3 1.37 #19 12.5 1.19 #20 16.1 1.05 #21 13.3 1.32 #22 4.9 1.03 #23 8.8 1.12 #24 9.5 1.70 plot(blood.glucose,short.velocity) ###Correlation cor(blood.glucose,short.velocity) #[1] NA cor(blood.glucose,short.velocity,use="complete.obs") #[1] 0.4167546 cor.test(blood.glucose,short.velocity) ###Pearson's product-moment correlation #data: blood.glucose and short.velocity #t = 2.101, df = 21, p-value = 0.0479 #alternative hypothesis: true correlation is not equal to 0 #95 percent confidence interval: # 0.005496682 0.707429479 #sample estimates: # cor #0.4167546 ### lm(short.velocity~blood.glucose) #Call: #lm(formula = short.velocity ~ blood.glucose) #Coefficients: # (Intercept) blood.glucose # 1.09781 0.02196 ##Summary summary(lm(short.velocity~blood.glucose)) #Call: #lm(formula = short.velocity ~ blood.glucose) #Residuals: # Min 1Q Median 3Q Max -0.40141 -0.14760 -0.02202 0.03001 0.43490 #Coefficients: # Estimate Std. Error t value Pr(>|t|) #(Intercept) 1.09781 0.11748 9.345 6.26e-09 *** #blood.glucose 0.02196 0.01045 2.101 0.0479 * --- Signif. codes: 0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1 #Residual standard error: 0.2167 on 21 degrees of freedom # (1 observation deleted due to missingness) #Multiple R-squared: 0.1737, Adjusted R-squared: 0.1343 #F-statistic: 4.414 on 1 and 21 DF, p-value: 0.0479 ###Scatter Plot plot(blood.glucose,short.velocity) abline(lm(short.velocity~blood.glucose)) lm.velo <- lm(short.velocity~blood.glucose) lm.velo ##Call: #lm(formula = short.velocity ~ blood.glucose) #Coefficients: # (Intercept) blood.glucose # 1.09781 0.02196 ###Fitted Values fitted(lm.velo) # 1 2 3 4 5 6 7 8 #1.433841 1.335010 1.275711 1.526084 1.255945 1.214216 1.302066 1.341599 9 10 11 12 13 14 15 17 1.262534 1.365758 1.244964 1.212020 1.515103 1.429449 1.244964 1.190057 18 19 20 21 22 23 24 1.324029 1.372346 1.451411 1.389916 1.205431 1.291085 1.306459 ## predict(lm.velo) # 1 2 3 4 5 6 7 8 #1.433841 1.335010 1.275711 1.526084 1.255945 1.214216 1.302066 1.341599 # 9 10 11 12 13 14 15 17 #1.262534 1.365758 1.244964 1.212020 1.515103 1.429449 1.244964 1.190057 # 18 19 20 21 22 23 24 #1.324029 1.372346 1.451411 1.389916 1.205431 1.291085 1.306459 ### predict(lm.velo,int="c") # fit lwr upr #1 1.433841 1.291371 1.576312 #2 1.335010 1.240589 1.429431 #3 1.275711 1.169536 1.381887 #4 1.526084 1.306561 1.745607 #5 1.255945 1.139367 1.372523 #6 1.214216 1.069315 1.359118 #7 1.302066 1.205244 1.398889 #8 1.341599 1.246317 1.436881 #9 1.262534 1.149694 1.375374 #10 1.365758 1.263750 1.467765 #11 1.244964 1.121641 1.368287 #12 1.212020 1.065457 1.358583 #13 1.515103 1.305352 1.724854 #14 1.429449 1.290217 1.568681 #15 1.244964 1.121641 1.368287 #17 1.190057 1.026217 1.353898 #18 1.324029 1.230050 1.418008 #19 1.372346 1.267629 1.477064 #20 1.451411 1.295446 1.607377 #21 1.389916 1.276444 1.503389 #22 1.205431 1.053805 1.357057 #23 1.291085 1.191084 1.391086 #24 1.306459 1.210592 1.402326 resid(lm.velo) # 1 2 3 4 5 6 # 0.326158532 0.004989882 -0.005711308 -0.056084062 0.014054962 0.275783754 # 7 8 9 10 11 12 # 0.007933665 -0.251598875 -0.082533795 -0.145757649 0.005036223 -0.022019994 # 13 14 15 17 18 19 # 0.434897199 -0.149448964 0.275036223 -0.070057471 0.045971143 -0.182346406 # 20 21 22 23 24 #-0.401411486 -0.069916424 -0.175431237 -0.171085074 0.393541161 res<-resid(lm.velo) res shapiro.test(res) # Shapiro-Wilk normality test #data: res #W = 0.92413, p-value = 0.08173 plot(res)