Questions and Answers of Regression Analysis

The variance of the predicted response in a linear regression model is a minimum at the average value of the predictor variable.a. Trueb. False
The confidence interval on the mean response at a particular value of the predictor variable is always wider than the prediction interval on a new observation at the same point.a. Trueb. False
The method of least squares ensures that the estimators of the slope and intercept in a linear regression model are best linear unbiased estimator.a. Trueb. False
For any simple linear regression model that has an intercept, the sum of the residuals is always zero.a. Trueb. False
How does the use of a multiple regression model affect the number of degrees of freedom in a regression model? Contrast your response with that involving a simple regression model.
Provide an interpretation of a partial regression coefficient. What additional condition must be imposed that is not required in a simple regression model?
Explain the role the adjusted coefficient of determination plays in a multiple regression model. What value does it contribute to the interpretation of the model? What does it adjust for and why is
Define multicollinearity. Fully describe the problems it can cause and the effect each has on the model.
Discuss the various methods to detect multicollinearity. What advantages and disadvantages does each method of detection offer?
How can the ill-effects of multicollinearity be mitigated? Describe each potential remedy and note the advantages and disadvantages of each.
Define the Variance Inflation Factor. What function does it perform in regression analysis?
Describe fully how the Variance Inflation Factor for a variable can be determined.
How does the R2 value found in a VIF test differ from that for the entire model?
What is meant by Analysis of Variance? What is its purpose? What exactly is the hypothesis in an ANOVA test? What does it mean if the null is not rejected? How do you interpret the rejection of the
How is the F-value in an ANOVA calculated? Why does a large Fvalue result in a rejection of the null? Use a graph in your response.
Clearly explain the three types of deviations as they pertain to an ANOVA test. Use a graph in the explanation.
What are the numbers of degrees of freedom for the regression sum of squares, error sum of squares, and the total sum of squares?
When must a dummy variable be used in a model? Provide your own original example of a dummy variable that might be used in a regression model.
A model to explain the per acre yield of grain uses rain fall, temperature, length of growing cycle in weeks, and four types of fertilizer used. Write the equation that would be used to estimate
Distinguish between an intercept dummy and a slope dummy. Provide a definition of both and examples of models that would incorporate each.
When would an interaction term be incorporated into a model? Explain its intended purpose. Provide an example of a regression model that would use an interaction term. Give an interpretation of the
As the product manager for a chemical company you must analyze the time required for a chemical reaction to be completed. A regression model to estimate time T measured in hours is provided here
El Dorado Industries sells perishable farm products to retailers throughout its market area. Recently, losses due to spoilage have reached unacceptable levels and the Quality Control Division has
Based on the Minitab printout of an ANOVA table from a regression model with two RHS variables:Analysis of Variancea. Fill in the missing values. Use the FINV and FDIST Excel functions if needed.b.
Given these results with t-values in parentheses for a model with 30 observations,find the p-values for all variables. Y =3.2+ 6.55X, +2.58X, +7.66X, +12.33X (3.45) (2022) (1682) (2.403) (0.6198)
Access the data file AIRPORT, which contains data for the number of minutes late that flights arrived at Chicago O'Hare Airport (Y), the number of minutes late that flights departed to Chicago (X1),
An investment analyst wishes to explain his clients' rates of return on their portfolios using two variables measuring returns from stocks and three from bond mutuals. The results of an unrestricted
Part of an ANOVA table appears as seen here. The rest was obliterated by the Division Chief when he placed his morning coffee cup on the computer printout. But now he wants to know if the model as a
What is the critical F-value in the preceding problem at the 5% level?At the 1% level?
A production function for auto factories estimates output (Q) using as predictor variables labor (L), capital (K), and hours of training for all employees (T).a. Using your preferred software, access
An investment broker is interested in predicting stock dividends based on the three variables shown below in the partial Excel output. Public is whether the company is publically or privately held.
As energy costs skyrocket, customers of Burlington Power expressed concern over their home heating bills. The staff at Burlington selects a sample of n = 50 home owners to form a data set regressing
Draw a graph depicting the three living locations in the previous problem.Previous problem As energy costs skyrocket, customers of Burlington Power expressed concern over their home heating bills.
Man's Best Friend Dog Food Company plans to market a new dry dog chow in certain test cities around the nation. Primary interest rests on the weight gain it creates in various dog breeds. Data are
Discuss the characteristics residuals must exhibit to ensure that the regression model obey all the Gauss-Markov assumptions. Use graphical work in each case.
What is meant by the statement that error terms must display a constant variance? Use a graph in your answer.
Distinguish between homoscedasticity and heteroscedasticity. Use a graph.
What conditions are most likely to precipitate heteroscedasticity?
What is meant by a standardized regression coefficient? How is it used in regression analysis?
A model is reported to be Ŷ = 5 + 7.2A + 5.8B − 2.4C. The standard deviation of each is SY = 2.7, SA = 3.8, SB = 0.58, and SC = 6.5. Which variable, A, B, or C, is most influential in determining
Describe how backward elimination, forward selection, and stepwise regression operate to produce a model. What caution should be exercised in their use?
A model with n = 65 observations is reported as seen below with tvalues in parentheses. Y is expressed in thousands, X1 in hundreds, X2 in thousands, and X3 in single units.a. What are the standard
Access the file PUBLIC TRADING. It contains data for the rate of return (ROR) measured in percentages, a risk level, the amount of the original investment (OIV), whether the stock is traded
King Soda, a nation-wide bottling company, notices that their bestselling product does not conform to the mean weight of 30 ounces in each container. Management suspects that the temperature in their
Discuss the destructive nature of the problems that beset the linear probability model.
Distinguish between a logit model and a limited dependent variable model. Give an example of each.
Write out and explain the equation for the cumulative distribution function.
Your colleague at work argues that the cumulative logistic distribution function is linear in the parameters but not in the variables. Is she correct? Explain your response.
Explain the statement, “the cumulative logistic distribution function is linear in the logs.” Use an equation in your answer.
Why is Equation (6.1.3) called the “log of the odds ratio”? In 1 - P = , = B + BX + BX + + BX (6.1.3)
What exactly does the coefficient of Equation (6.1.3) measure? In 1 - P = Z = A + BX + BX + + BX (6.1.3)
Why is R2 not a good measure of fit in a logit model?
Explain the nature of the log-likelihood ratio. What does it measure?
Explain why a low log-likelihood ratio indicates a better fit.
Discuss the limitations imposed by the restrictive assumption placed on the discriminant model.
What is the role of the centroid and how is it formed?
How is the cutoff score computed and what role does it play in modeling?
What is meant by cross-validation in a discriminant model? Why is it done and how does it work?
What role does the Maximum Chance Criterion play in discriminant analysis?
How is PRESS'S Q-statistic used in discriminant analysis?
Over the last few years Standard and Poor's, a financial services company and credit-rating agency, has downgraded, or threatened to downgrade, the credit rating for several nations around the globe.
Investment analysts for a large international consulting firm in Paris estimate a logit model to predict the likelihood their major clients will withdraw their account and move to a competing firm.
Thirty shipments by TransAtlantic Express designed to predict the likelihood a shipment would reach its port of destination on time yields the following information:a. What is the likelihood a
A logit model with 50 observations and three RHS variables reports a χ2 of 13.7, a −2 log-likelihood for the restricted model of 42.7, and a −2 log-likelihood for the unrestricted model of 29.
The dean of a business school wants to identify students most likely to successfully complete a master's degree in economics on the basis of a test score and their rank in undergraduate school. The
Write and explain the formula you would use to correct for heteroscedasticity if the population variances were known. Why and how does this process correct for heteroscedasticity?
Prove that after transforming the data as explained in the question above, homoscedasticity prevails.Question aboveWrite and explain the formula you would use to correct for heteroscedasticity if the
Why is the solution to heteroscedasticity as proposed in the first two questions unlikely to occur?
Explain the meaning behind Equation (7.3.4). What is it telling you to do? Var(e,)=o=oX (7.3.4)
Explain how the transformation described in this section turns the pretransformed slope into the intercept and vice versa.
Using your preferred computer software and the data from problem 6 in Section 7.2, correct for heteroscedasticity. Assume Var (εi) = σ2 i =σ2X2 i, where Xi is bank balances.Data from problem 6 in
Define elasticity. How is it measured?
Explain how the use of logs produces a measure of elasticity.
Your research assistant has discovered that the model you have been working with to explain changes in shipping costs suffers from heteroscedasticity. She bemoans the loss of time and the increased
As a city planner for the National Health Service in London, England, your duties include reconciling differences with the provisions for healthcare elsewhere in the United Kingdom. Would you expect
Why are cross-sectional studies less likely to be afflicted with autocorrelation but highly subject to heteroscedasticity?
Clearly describe the steps that must be taken to test for heteroscedasticity using the tests described in this chapter. What advantages and disadvantages does each offer?
Explain how the slope coefficient and the intercept become interchanged when correcting for heteroscedasticity.
Define and give examples of elasticity. Clearly explain how the use of logs results in measures of elasticity.
Prove that weighted least squares result in homoscedastic models. Use all necessary equations in your response.
Distinguish between pure and impure heteroscedasticity.
Discuss the relationship between elasticity and the manner in which price changes affect total revenue. If a firm's goal is to raise revenues, should it increase or decrease price if demand is
Demonstrate using the proper formulas discussed in this chapter how a double-log model gives the measure of elasticity for a function.
Define autocorrelation. Why is it more likely to occur with the use of time series data than with cross-sectional data?
Distinguish between first-order and higher-order autocorrelation. Give examples of each.
Why does the cyclical nature of economic and business activity tend to result in autocorrelation? What does the issue of “stickiness” have to do with this matter?
Distinguish between positive and negative autocorrelation. Define and give examples. How might a graph of each appear?
Examine the graphs below and comment on your perception of whether autocorrelation might be an issue and if so, is it positive or negative autocorrelation? Error 15 10 5 0 -5 -10 -15 -20 0 1 2 3 4
What are the primary causes of autocorrelation? Which is more difficult for the researchers to correct for?
How does an omitted variable affect the error term in a model and what implications does that have for autocorrelation?
Why does “stickiness” occur more often in time series data?
Why is autocorrelation more likely to occur with time series data than with cross-sectional data? Distinguish between the two types of data, giving examples of each, in your response.
What two conditions must exist to ensure a model is properly specified? Give examples in both cases.
How might autocorrelation bias the coefficient estimates, bi?
How does autocorrelation impact the standard error of the coefficient estimate?
What is meant by bias in an estimator? What is meant by consistency of an estimator? What is the difference between an estimate and an estimator? Give examples.
Does autocorrelation promote inefficiency in estimators? Explain.
Explain how the Durbin-Watson statistic tests for autocorrelation.
Explain why Durbin-Watson values can distinguish between positive and negative autocorrelation.
Why does the Durbin-Watson fall between 0 and 4?

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