Please use excel and show all steps Cascade Manufacturing produces a compressor
ID: 3174049 • Letter: P
Question
Please use excel and show all steps
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.
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)
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
Question 1:
Hence the equation of the line is Estimated Cost=252.846+125.1236* Order size
SUMMARY OUTPUT Regression Statistics Multiple R 0.971941237 R Square 0.944669767 Adjusted R Square 0.943517054 Standard Error 477.8199431 Observations 50 ANOVA df SS MS F Significance F Regression 1 187105822.7 187105822.7 819.5184934 7.98013E-32 Residual 48 10958971.1 228311.898 Total 49 198064793.8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 252.84616 206.9780342 1.221608665 0.227821561 -163.3110696 669.0033896 -163.3110696 669.0033896 Order Size 125.1236336 4.370790281 28.62723342 7.98013E-32 116.3355707 133.9116965 116.3355707 133.9116965