Cereal

install.packages("Stat2Data")

## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.5'
## (as 'lib' is unspecified)

library(Stat2Data)
data(Cereal)
attach(Cereal)

## The following object is masked _by_ .GlobalEnv:
## 
##     Cereal

cereal.lm = lm(Calories~Sugar)

Sugar Plot

plot(Calories~Sugar, main="Calories v. Sugar", xlab= "Sugar",ylab ="Calories")
abline(cereal.lm)

For every 1 gram of sugar, there is an increase in 2.4808 predicted calories, on average.

For 10 gram cereal, is it predicted to be approximately 112.285 calories

plot of residuals

plot(cereal.lm$fitted.values,cereal.lm$residuals,main="Residual Plot",ylab="Residuals",xlab="Predicted Calories")
abline(0,0)

The residual plot shows a random scatter, so the linear model appropriately fits the data.

Typical size of error for residuals is 19.27

The residual for 1 gram of sugar having 110 calories with predicted calories is approximately 20. Compared to the typical error, this is very likely.

histogram of residuals

hist(cereal.lm$residuals)

### normal plot

qqnorm(cereal.lm$residuals)
qqline(cereal.lm$residuals)

Looking at the histogram and normal plot of residuals, the linear regression model is a good summary for the relationship between sugar and calories in cereals.

Summary

summary(cereal.lm)

## 
## Call:
## lm(formula = Calories ~ Sugar)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.428  -9.832   0.245   8.909  40.322 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  87.4277     5.1627  16.935   <2e-16 ***
## Sugar         2.4808     0.7074   3.507   0.0013 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.27 on 34 degrees of freedom
## Multiple R-squared:  0.2656, Adjusted R-squared:  0.244 
## F-statistic:  12.3 on 1 and 34 DF,  p-value: 0.001296

Cereal

2025-09-23

Sugar Plot

For every 1 gram of sugar, there is an increase in 2.4808 predicted calories, on average.

For 10 gram cereal, is it predicted to be approximately 112.285 calories

plot of residuals

The residual plot shows a random scatter, so the linear model appropriately fits the data.

Typical size of error for residuals is 19.27

The residual for 1 gram of sugar having 110 calories with predicted calories is approximately 20. Compared to the typical error, this is very likely.

histogram of residuals

Looking at the histogram and normal plot of residuals, the linear regression model is a good summary for the relationship between sugar and calories in cereals.

Summary

About 24.4% of the variation in calories is explained by the Sugar content.

since p-val<0.01, the sugar content is a significant indicator for predicting calories in cereal.