library(readxl)
## Warning: package 'readxl' was built under R version 4.1.3
bmi <- read_excel("C:/Users/Lab pc/Downloads/bmi.xlsx")
View(bmi)
attach(bmi)
names(bmi)
## [1] "BMI" "Height" "Weight" "Gender"
full.model <- lm(BMI ~ Height + I(Height^2))
reduced.model <- lm(BMI ~ Height)
summary(full.model)
##
## Call:
## lm(formula = BMI ~ Height + I(Height^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9304 -1.7132 -0.1556 0.4968 5.2193
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 339.20890 384.79566 0.882 0.407
## Height -3.70155 4.54356 -0.815 0.442
## I(Height^2) 0.01073 0.01338 0.802 0.449
##
## Residual standard error: 2.966 on 7 degrees of freedom
## Multiple R-squared: 0.1193, Adjusted R-squared: -0.1324
## F-statistic: 0.4739 on 2 and 7 DF, p-value: 0.6412
summary(reduced.model)
##
## Call:
## lm(formula = BMI ~ Height)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8669 -1.9828 -0.2591 1.2393 5.2955
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 31.06284 18.34377 1.693 0.129
## Height -0.05974 0.10572 -0.565 0.588
##
## Residual standard error: 2.899 on 8 degrees of freedom
## Multiple R-squared: 0.03838, Adjusted R-squared: -0.08182
## F-statistic: 0.3193 on 1 and 8 DF, p-value: 0.5875
#partial f test
anova(reduced.model , full.model)
## Analysis of Variance Table
##
## Model 1: BMI ~ Height
## Model 2: BMI ~ Height + I(Height^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 8 67.245
## 2 7 61.589 1 5.6558 0.6428 0.449
model1 <- lm(BMI ~ Height + Gender + Weight)
model2 <- lm(BMI ~ Height + Weight + Gender)
anova(model1,model2)
## Analysis of Variance Table
##
## Model 1: BMI ~ Height + Gender + Weight
## Model 2: BMI ~ Height + Weight + Gender
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 6 0.52567
## 2 6 0.52567 0 8.8818e-16