Porsche Prices

Load Data

install.packages("Stat2Data")
## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.5'
## (as 'lib' is unspecified)
library("Stat2Data")
data("Cereal")
cereal = Cereal

a. Scatterplot

plot(cereal$Sugar, cereal$Calories)

The data appears to have a vaguely positive linear relationship between Sugar and Calories in Cereal.

b. LSRL

attach(cereal)
## The following object is masked _by_ .GlobalEnv:
## 
##     Cereal
cereal.lm = lm(Calories~Sugar)  
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
plot(Calories~Sugar)
abline(cereal.lm)

The LSRL for Sugar in Cereal according to Calories is y = 87.4277 + 2.4808x

c. Interpret Slope

For every increase in one gram of sugar, the predicted amount of calories in the cereal increases by 2.4808 kCal.”

d. Predict 10 grams of Sugar

The fitted model would predict that for a cereal with 10 grams of sugar, the total number of calories predicted is 112.2357 calories.

e. Size of Typical Error

The size of a typical error when predicting calories from sugar content is 19.27.

f. Residuals Plot

Residual = Actual - Predicted

Residual = 110 - 89.9085

Residual = 20.0915

g. Residual Interpretation

The number of calories for just one gram of sugar in the Cherrios cereal box is 20.0915 more than predicted.

h. Is the Lin Reg Model a good summary?

Scatterplot

plot(Calories~Sugar)
abline(cereal.lm)

The scatterplot shows a very slight linear, positive relationship between number of Calories in a cereal box in relation to the number of grams of sugar.

Plot of residuals vs fitted data

plot(cereal.lm$fitted.values, cereal.lm$residuals)  
abline(0,0)

The residual plot shows no apparent pattern, indicating the linear model is a good fit for the relationship between cereal calories and sugar content.

Histogram of residuals

hist(cereal.lm$residuals, breaks = 10)

The histogram appears to be uni modal and roughly symmetric. Since the residual plot for cereal sugar content and cereal calories is roughly normally distributed, we have some confidence that a linear model may fit the data best.

QQ Plot

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

#### The