R Notebook

library(s20x)
asphalt.df = read.table("asphalt.txt", header = TRUE)
pairs20x(asphalt.df)

asphalt.fit1 = lm(LMS ~ SHRSUS + ASPH + LST, data = asphalt.df)
eovcheck(asphalt.fit1)

summary(asphalt.fit1)     

Call:
lm(formula = LMS ~ SHRSUS + ASPH + LST, data = asphalt.df)

Residuals:
   Min     1Q Median     3Q    Max 
-7.282 -3.856 -2.236  2.749 13.989 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   4.2485     8.7316   0.487    0.631
SHRSUS       -8.4970     9.9639  -0.853    0.402
ASPH          0.4245     0.3368   1.260    0.220
LST          -0.1953     0.1705  -1.146    0.263

Residual standard error: 6.273 on 24 degrees of freedom
Multiple R-squared:  0.2887,    Adjusted R-squared:  0.1997 
F-statistic: 3.246 on 3 and 24 DF,  p-value: 0.03954

asphalt.fit2 = lm(LMS ~ ASPH + LST, data = asphalt.df)
summary(asphalt.fit2) 

Call:
lm(formula = LMS ~ ASPH + LST, data = asphalt.df)

Residuals:
   Min     1Q Median     3Q    Max 
-8.246 -3.517 -1.851  2.606 14.085 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)  -1.0443     6.1080  -0.171   0.8656  
ASPH          0.3710     0.3291   1.127   0.2703  
LST          -0.2639     0.1495  -1.766   0.0897 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.239 on 25 degrees of freedom
Multiple R-squared:  0.2671,    Adjusted R-squared:  0.2085 
F-statistic: 4.556 on 2 and 25 DF,  p-value: 0.02056

asphalt.fit3 = lm(LMS ~ LST, data = asphalt.df)
modcheck(asphalt.fit3) 

summary(asphalt.fit3) 

Call:
lm(formula = LMS ~ LST, data = asphalt.df)

Residuals:
   Min     1Q Median     3Q    Max 
-9.606 -3.781 -2.097  3.588 13.797 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)   2.4270     5.3024   0.458  0.65096   
LST          -0.3539     0.1271  -2.786  0.00984 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.271 on 26 degrees of freedom
Multiple R-squared:  0.2298,    Adjusted R-squared:  0.2002 
F-statistic: 7.759 on 1 and 26 DF,  p-value: 0.00984

confint(asphalt.fit3)

                 2.5 %      97.5 %
(Intercept) -8.4723139 13.32636819
LST         -0.6150702 -0.09274938

# Predictions of the AVERAGE LMS -> interval = "confidence"
pred.df = data.frame(SHRSUS = c(0.2, 0.5), ASPH = c(16, 18), LST = c(-20, -20))
predict(asphalt.fit3, pred.df, interval = "confidence")

       fit      lwr      upr
1 9.505223 3.580811 15.42963
2 9.505223 3.580811 15.42963