3 Page Essay - Explain the correlation of data points to a given equation.

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Review Figures 4.4A, 4.4B, and 4.4C on page 120 (See below). What assumptions are being shown in these figures?

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**Make sure to cite any references used. The reference for the textbook pages used in this assignment is: (Please add the page numbers 119-120 into citation)

Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2015). Quantitative analysis for management (12th ed.). Upper Saddle River, NJ: Pearson.

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· FYI

· The page you see below this message is page 119 from the textbook, For you to better read the text I put the text you see in the bottom of the page 119 in readable text below with a cut out of the graph on 119 so it could be read easier (scroll down). Page 120 is located below page 119 (see below) I don’t know if the text on 119 has anything to do with the graph on the same page?

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Page 119 in textbook

Page 119 in textbook

IN ACTION - Using Regression as part of Improvement Initiative at Trane/Ingersoll Rand

Trane U.S. Inc. is a brand of Ingersoll Rand and is a leader in both home and commercial air conditioning. In an effort to improve quality and efficiency, the company consolidated its manufacturing of evaporator and condenser coils into one location in South Carolina.

A key part of the coil unit is a header, which controls the flow of water or refrigerant through the coil. With about 120 unique headers produced on each shift, with increased demand for their air conditioners due to federal refrigerant standards, and with growing pressure to reduce costs, Trane began an improvement initiative in 2010. Value stream mapping, a lean manufacturing technique, was used to visualize the entire process and identify waste in the system.

A new layout was suggested to improve processing and reduce the overall time of production. To predict how well the new layout would perform in the manufacture of the headers, data was collected about the time to move materials into position, time to set up a job, time to set up a machine, and time to process a job. Several regression models were developed to determine which job characteristics were most significant in the various times involved in processing, and to measure the variability in times.

These were used in simulation models that were developed to determine the overall impact of the new layout and to determine where bottlenecks might occur. One of the bottle necks, at a robotic machine for welding, was eliminated by re- tooling the robot to allow the machine operator to operate both sides of the robot. This enables the robot to process two headers simultaneously. The improvement initiatives from this project are estimated to save over $700,000 per year. This project highlighted the importance of data-based analytics and lean manufacturing tools in identifying the improvement tactics for complex value streams. The company plans similar improvement initiatives for other value streams in the future.

Source: Based on John B. Jensen, Sanjay L. Ahire, and Manoj K. Malhotra "Trane/Ingersoll Rand Combines Lean and Operations Research Tools to Rede sign Feeder Manufacturing

Page 119

Page 120

The text on page 120 is as follows:

4.5 CHAPTER 4. REGRESSION MODELS Assumptions of the Regression Model If we can make certain assumptions about the errors in a regression model, we can calculate tests to determine if the model is useful. The following assumptions are made about the errors:

1. The errors are independent

2. The errors are normally distributed

3. The errors have a mean of zero.

4. The errors have a constant variance (regardless of the value of X).

It is possible to check the data to see if these assumptions are met. Often a plot of will highlight any glaring violations of the assumptions. When the errors (residual against the independent variable, the pattern should appear random.

Figure 4.4 presents some typical error patterns, with Figure 4.4A displaying expected when the assumptions are met and the model is appropriate. The errors no discernible pattern is present.

Figure 4.4B demonstrates an error pattern in which increase as X increases, violating the constant variance assumption.

Figure 4.4C A plot of the errors may highlight problems with the model. plot of the residuals

FIGURE 4.4A Pattern of Errors Indicating Randomness Error

FIGURE 4.4B Nonconstant Error Variance Error

FIGURE 4.4C Errors Indicate Relationship Is Not Linear Error