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library(car)setwd("/Volumes/KINGSTON/MedScholars/Data")
d1 <- read.csv("Data analysis workbook4.csv")Regression with ERC alone:
lm0 <-lm (DEL~ERC_avg,data = d1)
summary (lm0)##
## Call:
## lm(formula = DEL ~ ERC_avg, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6709 -0.2376 0.0365 0.2509 0.6273
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.6389 0.2305 -2.771 0.00675 **
## ERC_avg 0.5097 0.1024 4.978 2.99e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3008 on 92 degrees of freedom
## (5 observations deleted due to missingness)
## Multiple R-squared: 0.2122, Adjusted R-squared: 0.2036
## F-statistic: 24.78 on 1 and 92 DF, p-value: 2.989e-06Regression with ERC, SRLM, and tau:
lm1 <-lm (DEL~tau+SRLM_avg+ERC_avg,data = d1)
summary(lm1)##
## Call:
## lm(formula = DEL ~ tau + SRLM_avg + ERC_avg, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43768 -0.12118 -0.02816 0.14740 0.44290
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.7515987 0.3453342 -2.176 0.034581 *
## tau -0.0004136 0.0001188 -3.483 0.001084 **
## SRLM_avg 2.1400044 0.5422291 3.947 0.000263 ***
## ERC_avg 0.1045405 0.1321209 0.791 0.432774
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2154 on 47 degrees of freedom
## (48 observations deleted due to missingness)
## Multiple R-squared: 0.5925, Adjusted R-squared: 0.5665
## F-statistic: 22.78 on 3 and 47 DF, p-value: 2.989e-09Regression with SRLM and tau:
lm2 <-lm(DEL~SRLM_avg+tau,data = d1)
summary(lm2)##
## Call:
## lm(formula = DEL ~ SRLM_avg + tau, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4184 -0.1262 -0.0076 0.1442 0.4536
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.6110289 0.2949763 -2.071 0.043715 *
## SRLM_avg 2.3070453 0.4974953 4.637 2.74e-05 ***
## tau -0.0004233 0.0001177 -3.598 0.000757 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2145 on 48 degrees of freedom
## (48 observations deleted due to missingness)
## Multiple R-squared: 0.5871, Adjusted R-squared: 0.5699
## F-statistic: 34.12 on 2 and 48 DF, p-value: 6.045e-10Regression with SRLM alone:
lm3 <-lm(DEL~SRLM_avg,data = d1)
summary(lm3)##
## Call:
## lm(formula = DEL ~ SRLM_avg, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.70228 -0.19839 -0.05688 0.19193 0.71350
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.9749 0.2035 -4.791 6.10e-06 ***
## SRLM_avg 2.7472 0.3785 7.259 1.06e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2725 on 95 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.3568, Adjusted R-squared: 0.35
## F-statistic: 52.69 on 1 and 95 DF, p-value: 1.06e-10Regression predicting DEL with SRLM and ERC:
lm3a <-lm(DEL~ERC_avg+SRLM_avg,data = d1)
summary(lm3a)##
## Call:
## lm(formula = DEL ~ ERC_avg + SRLM_avg, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.60222 -0.17348 -0.04893 0.19674 0.57996
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.36232 0.24088 -5.656 1.78e-07 ***
## ERC_avg 0.30944 0.09659 3.204 0.00187 **
## SRLM_avg 2.18849 0.40082 5.460 4.09e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2625 on 91 degrees of freedom
## (5 observations deleted due to missingness)
## Multiple R-squared: 0.4066, Adjusted R-squared: 0.3935
## F-statistic: 31.17 on 2 and 91 DF, p-value: 4.875e-11Regression comparing SRLM and ERC:
lm3b <-lm(ERC_avg~SRLM_avg,data = d1)
summary(lm3b)##
## Call:
## lm(formula = ERC_avg ~ SRLM_avg, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.59274 -0.19930 -0.02754 0.17659 0.79061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.3321 0.2159 6.169 1.72e-08 ***
## SRLM_avg 1.6737 0.4012 4.172 6.73e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2872 on 94 degrees of freedom
## (3 observations deleted due to missingness)
## Multiple R-squared: 0.1562, Adjusted R-squared: 0.1472
## F-statistic: 17.4 on 1 and 94 DF, p-value: 6.733e-05Checking for co-linearity between SRLM and ERC:
vif(lm3a)## ERC_avg SRLM_avg
## 1.168485 1.168485Checking for co-linearity between tau, SRLM and ERC:
vif(lm1)## tau SRLM_avg ERC_avg
## 1.348563 1.572470 1.311566Regression with tau alone:
lm4 <-lm(DEL~tau,data = d1)
summary(lm4)##
## Call:
## lm(formula = DEL ~ tau, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.52396 -0.22445 0.07135 0.20551 0.46933
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7362508 0.0607696 12.12 2.37e-16 ***
## tau -0.0006964 0.0001213 -5.74 5.87e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2555 on 49 degrees of freedom
## (48 observations deleted due to missingness)
## Multiple R-squared: 0.4021, Adjusted R-squared: 0.3898
## F-statistic: 32.95 on 1 and 49 DF, p-value: 5.873e-07Regression with tau and ERC:
lm4a <-lm(DEL~tau+ERC_avg, data = d1)
summary(lm4a)##
## Call:
## lm(formula = DEL ~ tau + ERC_avg, data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.48677 -0.21911 0.05101 0.20398 0.45787
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0357077 0.3218560 0.111 0.9121
## tau -0.0006096 0.0001232 -4.949 9.58e-06 ***
## ERC_avg 0.3075566 0.1389505 2.213 0.0317 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2459 on 48 degrees of freedom
## (48 observations deleted due to missingness)
## Multiple R-squared: 0.4574, Adjusted R-squared: 0.4348
## F-statistic: 20.23 on 2 and 48 DF, p-value: 4.236e-07Regression accounting for interaction between tau and SRLM:
lm5 <-lm(DEL~SRLM_avg+tau+I(SRLM_avg*tau),data = d1)
summary(lm5)##
## Call:
## lm(formula = DEL ~ SRLM_avg + tau + I(SRLM_avg * tau), data = d1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.36089 -0.13663 0.00956 0.11956 0.52094
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.299432 0.458968 -2.831 0.0068 **
## SRLM_avg 3.670779 0.858900 4.274 9.31e-05 ***
## tau 0.001851 0.001189 1.557 0.1262
## I(SRLM_avg * tau) -0.004659 0.002424 -1.922 0.0607 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2087 on 47 degrees of freedom
## (48 observations deleted due to missingness)
## Multiple R-squared: 0.6172, Adjusted R-squared: 0.5927
## F-statistic: 25.25 on 3 and 47 DF, p-value: 7.023e-10