library(s20x)
McDonald.df = read.table(file.choose(), header = TRUE)
head(McDonald.df)
#Put in data in as a working variable
price = McDonald.df$Price
energy = McDonald.df$Energy
plot(energy ~ price, main = "Energy versus Price of fastfood items", data = McDonald.df)
abline(McDonald.fit)
Exploratory Analysis: The data is very scattered at the bottom to middle with data point 5 at a very high price as well as energy provided. But in general, there seems to be a positive linear relationship between the price and the energy value.
#Fit model
McDonald.fit = lm(energy ~ price, data = McDonald.df)
#Check for equality of variance
eovcheck(energy ~ price)
As seen before, the data is scattered quite evenly but with 1 single data point 5 that might be influential.
#Normality check
normcheck(McDonald.fit)
The Q-Q test shows that the data fits into the linear model as well as the bell curve for most part, hence we used the Central Limit Theorem which makes the normality assumption for the data satisfactory.
#There was a data point that might be influential to the investigation, hence we check using Cook's distance plot.
cooks20x(McDonald.fit)
All data point Cook’s distance is within the 0.4 range with the exception of data point number 5, hence, the point should be removed from the data set.
#Create new model that doesn't have the point data 5
McDonaldnews.df <- McDonald.df[-c(5), ,drop = F]
#Fit the new model
McDonaldnew.fit1 = lm(energy ~ price, data = McDonaldnews.df)
#Summary
summary(McDonaldnew.fit1)
Call:
lm(formula = energy ~ price, data = McDonaldnews.df)
Residuals:
Min 1Q Median 3Q Max
-801.23 -294.28 60.52 191.58 865.33
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 168.11 154.58 1.088 0.289
price 284.37 35.67 7.973 6.24e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 402.5 on 22 degrees of freedom
Multiple R-squared: 0.7429, Adjusted R-squared: 0.7312
F-statistic: 63.57 on 1 and 22 DF, p-value: 6.245e-08
confint(McDonaldnew.fit)
2.5 % 97.5 %
(Intercept) -152.4617 488.6825
price 210.4043 358.3437
predEnergy.df = data.frame(price = (5.90))
predict(McDonaldnew.fit, predEnergy.df, interval = "prediction")
fit lwr upr
1 1845.917 978.0856 2713.749
Method and Assumption check The data in the plot of Energy versus Price shows that there is a positive linear relationship between the price paid for a McDonald item and the energy content of it. The observation appears to be independent. There is an almost constant scatter with 1 single data point that seems to be influential. The data set is satisfactory for the normality assumption. However, the data point 5 is ruled out as an influential data point though the Cook’s distance test (over 0.4), hence, it was remove for the final calculations. The final model fitted is: 〖energy〗_(i )= β_0+ β_1 ×price+ ε_i where ε_i (iid) ̃ N(0,σ^2).
Executive Summary The data set was collected by the Teaching Fellow of the energy content for a McDonald’s food item and its price. The aim is to predict the amount of energy content of the McDonald’s food item given its price based on the data set collected. There is a general positive linear relationship between the price of the food item and its energy content. On average, the higher the price for the food item, the higher its energy content.
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