Question

The cost of manufacturing one unit of a product (€Y) appears to vary randomly with the size of the batch manufactured (X units). On 8 separate days, 8 different batch sizes were manufactured and the cost per unit calculated. The batch sizes and cost per unit are contained in the Production.txt file.

Production.txt file contents:

"X" "Y"
"1" 100 835.91
"2" 200 978.44
"3" 300 634.45
"4" 400 687.01
"5" 500 771.14
"6" 600 459.71
"7" 700 392.78
"8" 800 296.46

a) Create a files called Production.txt and import it into R. Report the code you used below.

R Code:

b) Fit a simple linear regression model to the Production.txt data, where the cost per unit is the response variable and the batch size is the predictor variable. Report the code you used to fit this model and print the output to the screen. Also, report the least squares estimates of the intercept and the slope of the fitted regression line.

R Code:

Intercept:

Slope:

c) What is the relationship between X and Y.
Positive or Negative?

d) Predict the production cost per unit for a batch of 340 units.

Answer:

R Code:

Answer 1

We will use read.table function of R to read the file.

Production=read.table("Production.txt")

model<-lm(data = Production,formula = Y~X) #This is the function for creating a linear regression model . The formula part # says that we need to predict the variaable Y in terms of variable X

summary(model)

library(ggplot2)
ggplot(Production,aes(x=X,y=Y)) + geom_point() + geom_smooth(method = lm,formula = y~x,se = F)

#This is to just depict the least squares line on a graph ( This is just for Your understanding)

predicted=predict(model,newdata = data.frame(X=340)) #We use the R's predict function which takes in the model as the #first argument and the second argument as the new data point(s) (as a data frame) we want to predict the value for the #response variable.

predicted

As it is clear from the output that the estimate for intercept is 1014.7307 and for slope is -0.8505

To get the relation, we substitute these values in the general equation-

Y=(slope_estimate)X + (intercept_estimate)

You can substitute these values.

To get a visual idea here is a plot made using the ggplot (You need to install the ggplot2 library for using this command) command above-

For the prediction part -