Exam 9: Regression Analysis

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?

Exhibit 9.3 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.Test the significance of the model and explain which values you used to reach your conclusions.

The terms b₀ and b₁ are referred to as

Exhibit 9.6 The partial regression output below applies to the following questions. -Refer to Exhibit 9.6.What is the F-statistic value?

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

R² is calculated as

The regression residuals are computed as

Project 9.1 ? Test Stand Cost Analysis Estimation 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. Test Stand Product Cost Estimation The data estimates for the three cost proposal due Monday is the following: Estimates for New Lines Lines of Reparable Primary Deployed Estmated Estmated Code Items Functions Sites Sales Life R\&M 1 5000 7 4 400 4000 7.5 0.965857 2 7500 5 5 450 4500 8.5 0.976311 3 34n0 6 3 375 3750 6 0.930541 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.

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

What is the correct range for R² values?

In time series regression analysis

Which of the following best describes the relationship between cost and accuracy in forecasting?

Exhibit 9.1 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.Interpret the meaning of R Square in cell B3 of the spreadsheet.

Exhibit 9.2 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.Predict the mean pressure for a temperature of 120 degrees.

The adjusted R² statistic

Exhibit 9.3 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.Predict the mean number of calories consumed by a 19 year old man.

Which of the following cannot be negative?

A persistent upward or downward movement of data is called

Assume you have chosen to use all three variables in your model.Test the significance of the model and explain which values you used to reach your conclusion.

Why do we create a scatter plot of the data in regression analysis?