Weight against calories consumed
library(e1071)
## Warning: package 'e1071' was built under R version 3.5.1
Weight_Calories <- read.csv("E:\\Data Science\\data science\\assignments\\Simple Linear Regression\\calories_consumed.csv")
colnames(Weight_Calories) <-c("WeightInGrams", "Calories")
attach(Weight_Calories)
dim(Weight_Calories)
## [1] 14 2
#First Moment Busisness Decision
summary(Weight_Calories)
## WeightInGrams Calories
## 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
#Second Moment Busisness Decision
var(WeightInGrams)
## [1] 111350.7
var(Calories)
## [1] 565668.7
sd(WeightInGrams)
## [1] 333.6925
sd(Calories)
## [1] 752.1095
#Thrid Moment Busisness Decision
skewness(WeightInGrams)
## [1] 0.9994639
skewness(Calories)
## [1] 0.5212708
#Fourth Moment Busisness Decision
kurtosis(WeightInGrams)
## [1] -0.506441
kurtosis(Calories)
## [1] -0.9277095
plot(Calories, WeightInGrams, col = "Blue")
# Correlation coefficient for Weight and calories
cor(Calories, WeightInGrams)
## [1] 0.946991
slr <- lm(WeightInGrams~Calories)
confint(slr, level = 0.95)
## 2.5 % 97.5 %
## (Intercept) -845.4266546 -406.0780569
## Calories 0.3305064 0.5098069
predict(slr, interval = "predict")
## Warning in predict.lm(slr, 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
summary(slr)
##
## Call:
## lm(formula = WeightInGrams ~ Calories)
##
## 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 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
# R-squared value for the above model is 0.8968.
# The R-sqaured value is higher - Weight and Calories model is good.