simple linear regration
dt <- read.csv("E:\\EXCELR ASSIGMENTS\\delivery_time (1).csv") # choose the wc-at.csv data set
View(dt)
#colnames(dt)<- c("dt","st") to change the colounm name
attach(dt)
plot(Delivery.Time,Sorting.Time)
# Correlation coefficient value for Waist and Addipose tissue
cor(Delivery.Time,Sorting.Time)
## [1] 0.8259973
reg<-lm(Sorting.Time~Delivery.Time)
summary(reg)
##
## Call:
## lm(formula = Sorting.Time ~ Delivery.Time)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.1388 -1.0014 -0.1045 0.5521 3.3507
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.75667 1.13395 -0.667 0.513
## Delivery.Time 0.41374 0.06477 6.387 3.98e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.47 on 19 degrees of freedom
## Multiple R-squared: 0.6823, Adjusted R-squared: 0.6655
## F-statistic: 40.8 on 1 and 19 DF, p-value: 3.983e-06
confint(reg,level = 0.95)
## 2.5 % 97.5 %
## (Intercept) -3.1300583 1.6167115
## Delivery.Time 0.2781691 0.5493182
predict(reg,inteval="predict")
## 1 2 3 4 5 6 7
## 7.931943 4.828866 7.414763 9.173174 11.241892 5.594291 7.104456
## 8 9 10 11 12 13 14
## 3.173891 6.649338 7.001020 7.447863 3.691071 6.144570 4.001378
## 15 16 17 18 19 20 21
## 4.220662 5.399832 4.932302 6.736224 2.553276 6.620376 8.138815
# R-squared value for the above model is 0.667.
# we may have to do transformation of variables for better R-squared value
# Applying transformations
# Logarthmic transformation
reg_log<-lm(Delivery.Time~log(Sorting.Time)) # Regression using logarthmic transformation
summary(reg_log)
##
## Call:
## lm(formula = Delivery.Time ~ log(Sorting.Time))
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0829 -2.0133 -0.1965 0.9351 7.0171
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.160 2.455 0.472 0.642
## log(Sorting.Time) 9.043 1.373 6.587 2.64e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.873 on 19 degrees of freedom
## Multiple R-squared: 0.6954, Adjusted R-squared: 0.6794
## F-statistic: 43.39 on 1 and 19 DF, p-value: 2.642e-06
confint(reg_log,level=0.95)
## 2.5 % 97.5 %
## (Intercept) -3.97778 6.297147
## log(Sorting.Time) 6.16977 11.917057
predict(reg_log,interval="predict")
## Warning in predict.lm(reg_log, interval = "predict"): predictions on current data refer to _future_ responses
## fit lwr upr
## 1 21.98291 15.6099875 28.35584
## 2 13.69652 7.4628028 19.93023
## 3 17.36331 11.2049447 23.52167
## 4 21.03009 14.7287585 27.33143
## 5 21.98291 15.6099875 28.35584
## 6 17.36331 11.2049447 23.52167
## 7 18.75735 12.5700473 24.94466
## 8 11.09489 4.6786298 17.51115
## 9 21.98291 15.6099875 28.35584
## 10 21.03009 14.7287585 27.33143
## 11 19.96493 13.7271824 26.20268
## 12 13.69652 7.4628028 19.93023
## 13 18.75735 12.5700473 24.94466
## 14 11.09489 4.6786298 17.51115
## 15 11.09489 4.6786298 17.51115
## 16 13.69652 7.4628028 19.93023
## 17 17.36331 11.2049447 23.52167
## 18 18.75735 12.5700473 24.94466
## 19 7.42810 0.5911537 14.26505
## 20 18.75735 12.5700473 24.94466
## 21 15.71450 9.5493253 21.87967
# R-squared value for the above model is 0.6723.
# we may have to do different transformation better R-squared value
# Applying different transformations
# Exponential model
reg_exp<-lm(log(Delivery.Time)~Sorting.Time) # regression using Exponential model
summary(reg_exp)
##
## Call:
## lm(formula = log(Delivery.Time) ~ Sorting.Time)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.29209 -0.13364 0.02065 0.08421 0.41892
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.12137 0.10297 20.601 1.86e-14 ***
## Sorting.Time 0.10555 0.01544 6.836 1.59e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1755 on 19 degrees of freedom
## Multiple R-squared: 0.7109, Adjusted R-squared: 0.6957
## F-statistic: 46.73 on 1 and 19 DF, p-value: 1.593e-06
# R-squared value has increased from 0.67 to 0.7071
# Higher the R-sqaured value - Better chances of getting good model
# for Waist and addipose Tissue