Assignment 12
mydata <- read.csv("C:\\Users\\RISHI RAHUL\\Desktop\\DS\\2 SLR\\Assignment\\calories_consumed.csv")
attach(mydata)
# 1st, 2nd, 3rd, 4th Moment Business Decision
summary(mydata)
## Weight.gained..grams. Calories.Consumed
## Min. : 62.0 Min. :1400
## 1st Qu.: 114.5 1st Qu.:1728
## Median : 200.0 Median :2250
## Mean : 357.7 Mean :2341
## 3rd Qu.: 537.5 3rd Qu.:2775
## Max. :1100.0 Max. :3900
var(Weight.gained..grams.)
## [1] 111350.7
sd(Calories.Consumed)
## [1] 752.1095
library(e1071)
skewness(Weight.gained..grams.)
## [1] 0.9994639
kurtosis(Calories.Consumed)
## [1] -0.9277095
# Plotting
boxplot(Weight.gained..grams.)
boxplot(Calories.Consumed, horizontal = TRUE)
hist(Calories.Consumed)
qqnorm(Calories.Consumed)
qqline(Calories.Consumed)
plot(mydata)
cor(mydata)
## Weight.gained..grams. Calories.Consumed
## Weight.gained..grams. 1.000000 0.946991
## Calories.Consumed 0.946991 1.000000
# Model
model <- lm(Weight.gained..grams. ~ Calories.Consumed)
summary(model) # R Squared Value : 0.8968
##
## Call:
## lm(formula = Weight.gained..grams. ~ Calories.Consumed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -158.67 -107.56 36.70 81.68 165.53
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -625.75236 100.82293 -6.206 4.54e-05 ***
## Calories.Consumed 0.42016 0.04115 10.211 2.86e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 111.6 on 12 degrees of freedom
## Multiple R-squared: 0.8968, Adjusted R-squared: 0.8882
## F-statistic: 104.3 on 1 and 12 DF, p-value: 2.856e-07
model_log <- lm((Weight.gained..grams.) ~ log(Calories.Consumed))
summary(model_log) # R Squared Value : 0.8077
##
## Call:
## lm(formula = (Weight.gained..grams.) ~ log(Calories.Consumed))
##
## Residuals:
## Min 1Q Median 3Q Max
## -187.44 -142.96 23.13 113.20 213.82
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6955.7 1030.9 -6.747 2.05e-05 ***
## log(Calories.Consumed) 948.4 133.6 7.100 1.25e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 152.3 on 12 degrees of freedom
## Multiple R-squared: 0.8077, Adjusted R-squared: 0.7917
## F-statistic: 50.4 on 1 and 12 DF, p-value: 1.248e-05
model_exp <- lm(log(Weight.gained..grams.) ~ Calories.Consumed)
summary(model_exp) # R Squared Value : 0.8776
##
## Call:
## lm(formula = log(Weight.gained..grams.) ~ Calories.Consumed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.86537 -0.10532 0.02462 0.13467 0.42632
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.8386724 0.2994581 9.479 6.36e-07 ***
## Calories.Consumed 0.0011336 0.0001222 9.276 8.02e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3314 on 12 degrees of freedom
## Multiple R-squared: 0.8776, Adjusted R-squared: 0.8674
## F-statistic: 86.04 on 1 and 12 DF, p-value: 8.018e-07
confint(model,level=0.95)
## 2.5 % 97.5 %
## (Intercept) -845.4266546 -406.0780569
## Calories.Consumed 0.3305064 0.5098069
predict(model,interval="predict")
## Warning in predict.lm(model, interval = "predict"): predictions on current data refer to _future_ responses
## fit lwr upr
## 1 4.482599 -258.20569 267.1709
## 2 340.607908 88.93791 592.2779
## 3 802.780209 533.81393 1071.7465
## 4 298.592245 46.63271 550.5518
## 5 424.639236 172.59086 676.6876
## 6 46.498263 -213.75953 306.7561
## 7 -37.533065 -302.93258 227.8664
## 8 172.545254 -82.18110 427.2716
## 9 550.686227 295.69632 805.6761
## 10 1012.858527 724.99432 1300.7227
## 11 75.909227 -182.81852 334.6370
## 12 172.545254 -82.18110 427.2716
## 13 508.670563 254.97398 762.3671
## 14 634.717554 376.22600 893.2091
# Simple Model has higher R Squared Value
model_final <- predict(model)
model_final
## 1 2 3 4 5 6
## 4.482599 340.607908 802.780209 298.592245 424.639236 46.498263
## 7 8 9 10 11 12
## -37.533065 172.545254 550.686227 1012.858527 75.909227 172.545254
## 13 14
## 508.670563 634.717554
rmse <- sqrt(mean((model_final-Weight.gained..grams.)^2))
rmse
## [1] 103.3025
plot(model)
hist(residuals(model))
