Cascade Manufacturing produces a compressor motor for air conditioner units. The

Question

Cascade Manufacturing produces a compressor motor for air conditioner units. The company manufactures the motors to order by modifying the base model to meet the specifications requested by the customer. The motors are produced in a batch environment with the batch size equal to the number ordered. Marlene Jacobs is the plant manager for Cascade Manufacturing and she would like to know if there is any relationship between order size and cost of production. She had her quality control group randomly collect a sample of 50 customer orders and record the size of the order and the total production cost. The data collected are in the file "Cascade Manufacturing" and that file is attached. If there is a significant relationship between the size of the order and the production cost, Ms. Jacobs would like to be able to estimate production costs based on order size.

1. Use the sample data to develop a regression model with the order size as the independent variable and the cost as the dependent variable. (5 pts)

2. Test the significance of the overall regression model using a significance level of 0.05. (5 pts)

3. Cascade Manufacturing has just received an order from their largest customer for 80 motors. (10 pts)

a. Use the regression model from part 1 to provide a 90% confidence interval for the average cost of an order of 80 motors.

b. Again, using the regression model from part 1, produce a 90% prediction interval for the cost of this particular order.

4. This is the most important part: Write a memorandum to Ms. Jacobs.

a. Explain the coefficients of the regression model. (5 pts)

b. Explain parts 3a and 3b clearly defining the differences in the predictions.(5 pts) Do all your calculations in Excel

Order Size Total Cost 56 $     7,531 54 $     6,329 68 $     8,413 60 $     7,793 38 $     5,360 42 $     4,838 22 $     2,551 34 $     3,899 66 $     8,326 46 $     5,465 14 $     2,283 46 $     5,413 36 $     4,238 52 $     6,911 40 $     6,315 58 $     8,243 20 $     2,866 44 $     6,775 28 $     4,289 12 $     1,475 30 $     3,590 70 $     9,439 46 $     6,760 36 $     5,170 62 $     7,780 42 $     4,896 70 $     8,816 58 $     8,116 42 $     6,212 48 $     5,551 54 $     7,080 72 $     9,826 48 $     6,129 40 $     5,094 26 $     3,568 28 $     3,738 38 $     5,332 28 $     3,286 56 $     6,664 48 $     5,990 54 $     7,093 32 $     3,975 72 $     9,046 40 $     4,906 38 $     5,324 14 $     2,734 64 $     8,138 42 $     5,376 58 $     7,763 46 $     5,964

Explanation / Answer

We shall solve the first 4 parts of the question using the open source statistical software R. The complete R snippet is as

##########################################

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\cost.csv",header=TRUE)
str(data.df)
data.df$Total.cost<- as.numeric(data.df$Total.cost)

fit <- lm(Total.cost~Order.Size, data=data.df)

summary(fit)

newdata <- data.frame(Order.Size=80)

predict(fit,newdata,interval="confidence",level = 0.90)

predict(fit,newdata,interval="prediction" , level=0.90)

###############################################################

The results are

> summary(fit)

Call:
lm(formula = Total.cost ~ Order.Size, data = data.df)

Residuals:
Min 1Q Median 3Q Max
-707.78 -350.91 -83.65 322.46 1057.21

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 252.846 206.978 1.222 0.228
Order.Size 125.124 4.371 28.627 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 477.8 on 48 degrees of freedom
Multiple R-squared: 0.9447,   Adjusted R-squared: 0.9435
F-statistic: 819.5 on 1 and 48 DF, p-value: < 2.2e-16 , as p value is less than 0.05 hence the model is signifcant

>
> newdata <- data.frame(Order.Size=80) # get the data for the new order which is 80
>
> predict(fit,newdata,interval="confidence",level = 0.90)
fit lwr upr
1 10262.74 9980.632 10544.84
>
> ?predict()
>
> predict(fit,newdata,interval="prediction" , level=0.90)
fit lwr upr
1 10262.74 9413.123 11112.35

Please note that we can answer only 4 subparts of a quesiton at a time , as per the answering guidelines

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