Exam 9: Regression Analysis

The following questions are based on the problem description and spreadsheet below. A researcher is interested in determining how many calories young men consume. She measured the age of the individuals and recorded how much food they ate each day for a month. The average daily consumption was recorded as the dependent variable. She has developed the following Excel spreadsheet of the results. -Refer to Exhibit 9.3. What is the estimated regression function for this problem? Explain what the terms in your equation mean

The partial regression output below applies to the following questions. -Refer to Exhibit 9.7. What is the SS for Residual and MS for Residual?

In the equation Y = $\beta$ ₀ + $\beta$ ₁ X_1i + $\varepsilon$ , $\beta$ 0₁ is

The reason an analyst creates a regression model is

The standard error measures the

The following questions are based on the problem description and spreadsheet below. A paint manufacturer is interested in knowing how much pressure (in pounds per square inch, PSI) builds up inside aerosol cans at various temperatures (degrees Fahrenheit). It has developed the following Excel spreadsheet of the results. -Refer to Exhibit 9.2. Test the significance of the model and explain which values you used to reach your conclusions.

When using the Regression tool in Excel the independent variable is entered as the

Which of the following represents a regression model?

Estimation errors are often referred to as

The error sum of squares term is used as a criterion for determining b₀ and b₁ because

The following questions are based on the problem description and spreadsheet below. A researcher is interested in determining how many calories young men consume. She measured the age of the individuals and recorded how much food they ate each day for a month. The average daily consumption was recorded as the dependent variable. She has developed the following Excel spreadsheet of the results. -Refer to Exhibit 9.3. Interpret the meaning of the "Lower 95%" and "Upper 95%" terms in cells F16:G16 of the spreadsheet.

Based on the following regression output, what conclusion can you reach about $\beta$ ₀?

The following questions are based on the problem description and spreadsheet below. A charitable organization wants to determine what type of people donate to charities like itself. The charity felt that a person's education (in years), annual income, ($1,000) and the number of children the person had were important variables to consider. The charity developed regression models for all of the possible combinations of these three variables but does not know what to do with the results. -Refer to Exhibit 9.4. Based on the data in the table which is the best model for the charity to use? Explain which values you used to reach your conclusion.

The researcher would like to build a prediction interval on the calories consumed by an 18 year old man. What formula should be entered in cells B17:F21 of the following spreadsheet to compute this prediction interval? Partial results of the Regression analysis of the data are provided below.

For a simple linear regression model, a 100(1 - $\alpha$ )% prediction interval for a new value of Y when X = X_h is computed as

In regression terms what does "best fit" mean?

The following questions are based on the problem description and spreadsheet below. A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results. -Refer to Exhibit 9.1. Provide a rough 95% confidence interval on the number of labor hours for a batch of 5 parts.

The following questions are based on the problem description and spreadsheet below. A company has built a regression model to predict the number of labor hours (Y_i) required to process a batch of parts (X_i). It has developed the following Excel spreadsheet of the results. -Refer to Exhibit 9.1. Test the significance of the model and explain which values you used to reach your conclusions.

An analyst has identified 3 independent variables (X₁, X₂, X₃) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R² value for the X₃ model the same as the R² value for the X₁ and X₃ model, but the Adjusted R² values differ?

Handel Manufacturing produces test stands for various maintenance functions ranging from automobile to jet airline testing stations. For years, their cost estimating function was based on a myriad of historical data fed into a cost analysis model that produced very accurate estimates of both development and support costs for various proposed test stands. James Mudd was a recent hire into the cost analysis shop. Unfortunately, during his first week on the job, James deleted the cost analysis database and failed to maintain a backup of the model. Fortunately, all is not lost. The computer support personnel can come in Monday and retrieve the model using their system backup tapes. Unfortunately, the cost proposals for three new test stand development and deployment projects are due first thing Monday morning. Since James recently left the company, you have been tasked to complete the cost estimate portion of the proposals. After much gnashing of your teeth, you settle down to make the best of what you initially believe is a losing situation. While studying James' files you find historical records on 25 recent test stand development and deployment projects. Rejuvenated, you realize you can succeed in this prematurely perceived doomed situation. All you need to do is analyze this historical data, develop some cost estimating functions using regression, and then use your regression models to develop estimates for the three projects due Monday. The historical data in the files is the following. The data estimates for the three cost proposal due Monday is the following: One thing unclear from reading the files was on the form of the cost estimating relationships contained within the lost cost analysis model. You are somewhat sure the regression models were not polynomial in form, but you are not certain of this fact. You are not even sure which variables were included in the model for development cost and which variables were included in the model for support costs. However, you are undaunted because you know you can develop accurate models and produce good cost estimates for each of the proposed projects. Develop appropriate models for development and for support costs. Use these models to develop cost estimates for each of the new lines of test stands. For each of these cost estimates provide 95% confidence intervals for the predicted values.