Questions and Answers of Regression Analysis

Why does a Durbin-Watson close to 2 indicate the absence of autocorrelation?
How does the Durbin-Watson h adjust in the test for autocorrelation?Under what condition(s) should it be used?
Under what conditions is the Durbin-Watson test unreliable in its search for autocorrelation?
How can a simple hypothesis test be used to test for autocorrelation?
How can a runs test for randomness be used to test for autocorrelation?
Given the residuals 4, −5, 6, −7, −2, 6, and −7, with k = 1, does autocorrelation exist at the 5% level? At the 1% level?
What is meant by generalized least squares (GLS)? How does it work to correct for autocorrelation?
What is “transformed” in the application of GLS? Describe how that transformation takes place.
How does the Prais-Winsten technique modify the GLS?
How can a lagged variable be used to mitigate the ill-effects of autocorrelation? Devise your own original model to illustrate.
What is first-differencing and how does it reduce the harm imposed on a model by the presence of autocorrelation? Devise your own original model to illustrate.
What happens to the standard errors of the regression coefficients in the presence of autocorrelation? Why is this likely to increase the probability of a Type II error?
Fully discuss the consequences of autocorrelation.
Discuss the advantages and disadvantages of each of the methods discussed in this chapter to transform data to deal with the problems of autocorrelation. Under what conditions would one method prove
What problems are caused by the presence of autocorrelation and how might they affect your model?
Explain clearly why the Durbin-Watson statistic ranges between 0 and 4.
How does autocorrelation increase the probability of a Type I error?Use a graph to fully explain.
Discuss in detail the steps that must be carried out to transform the data for the Cochrane-Orcutt method of correcting for autocorrelation.
Discuss the merits and drawbacks of each of the methods presented in the chapter to correct for autocorrelation.
Which of the following are: (1) quadratics, (2) polynomials, (3) both,(4) neither? A. Y=2X-4X B. Y-2X-4X C. Y=23X +0.59X -5x 2 D. Y=. E. Y=X- X X F. Y=5-- H. Y = 5+ X 20 G. Y+5 10 X-5
Can a cubic be a polynomial? Explain and give an example.
Are all quadratics polynomials? Give examples and explain your answer.
Are all polynomials quadratics? Give examples to support your answer.
Solve the following quadratic equations using all three methods demonstrated in this section. A. 12X2-52X+50 B. 10 + 18X-50X C. 10x14X-45 D. 2X210X+2
A revenue curve proves to be R = −X2 + 58X + 52, where X is output.Use the vertex to determine how many units of output the producer should sell to maximize revenue. Roughly graph the revenue
An average cost curve reports to be AC = 214 + 5X2 − 10X. At what level of output is average cost minimized?
Access the file PRODUCTION FUNCTION in which output is expressed as a function of the number of labor hours used in the production process. Graph the relationship with output on the vertical axis.
Access the file PRODUCTION FUNCTION 2 in which Input is used as an independent variable to explain changes in Output.a. Graph the relationship with Output on the vertical axis. What do you observe?b.
Access the file COST FUNCTION. It is a model in which the total cost of production is a function of factor inputs used in the production process.a. Graph the function. Comment on its likely
Access the file QUANTITY OF TEA. It contains data for the amount of tea purchased in 50 different cities during a selected month of the year 2009 in Ireland and the prices of both tea and coffee.
Economic theory is often concerned with utility functions that measure the satisfaction (utility) economic agents derive from participating in the market. A “risk-taker” is one who gains such
Economists use utility functions to assess the degree of utility or satisfaction consumers receive from consuming goods and services.The functions are derived using regression techniques and measure
Express the utility function in the previous problem in double-log terms. Does the expression confirm your answer to part C of the previous problem?Previous problemEconomists use utility functions to
Identify and give examples of the following terms:A. Polynomial.B. Quadratic.C. Second-order polynomial.D. Degrees of homogeneity.E. Increasing, decreasing, and constant returns to scale.F.
Describe the functions listed here. Under what conditions would each be appropriate? What are the characteristics of each?A. Double-log.B. Log-linear.C. Linear-log.D. Reciprocal.E. Exponential.F.
Solve the following quadratic equations using all three methods described in the chapter. A. 4X26X-8. B. 4X2 +5X-8. C. 0.8X-8.X. D. 0.8X+4X+ 12.
A firm's total revenue curve is estimated to be TR = −2.5Q2 + 15Q + 56. At what level of output should the firm operate to maximize revenue? What is TR at that point? What are the measures of TR
An average cost curve is found to be AC = 89.96 + 0.0179Q2 − 2.294Q. At what level of output is average cost minimized?
Given the AC curve in the previous problem, what is the total cost function?Previous problemAn average cost curve is found to be AC = 89.96 + 0.0179Q2 − 2.294Q. At what level of output is average
Corell Transport hauls heavy cargo between several major cities across the country. Rising fuel costs have caused a concern within upper management over future profit levels. Access the file CORELL
Given the data for Corell Transport in the previous problem, estimate the linear model and compare it with the non-linear, quadratic model.Previous problemCorell Transport hauls heavy cargo between
Residents of Lonesome, Arizona operate a co-operative agricultural center on the outskirts of town. Data for the quantity of kumquats sold in hundreds of pounds along with the total revenues and
The demand function for lumber products is thought to take the form P = AQ−b. Data were collected and displayed in the table below. One of your co-workers suggests a linear model regressing P on Q.
Utility functions measure the satisfaction consumers derive from the consumption of goods and services. They are often expressed as U = AQa 1Qb 2, where Q1 and Q2 are two commodities and A is a
Based on data compiled from the American Farmers Association, a non-profit organization established in 1983, demand for Idaho potatoes is estimated aswhile demand for imported agricultural crops
A Cobb-Douglas production function is Q = 12L.6K.5. What happens to Q if L increases by 1%? If K increases by 1%? What can you say about returns to scale?
With the Cobb-Douglas production function in problem 11, if L = 10 and K = 15, what is Q? If L increases by 1% what is the level of output, Q? What percentage increase is that? How does that compare
A semi-log (log-lin) consumption function states InC = 2 + 0.058I in which lnC is the log of consumption for a small national economy measured in billions of monetary units and / is the income
Based on the information in problem 13, if / is currently 10 what is C?If / increases by one unit to 11, what is C? What percentage increase is that?Problem 13A semi-log (log-lin) consumption
Given the data shown here for profits in 1,000s and tons sold:A. Compute the linear model and the log-linear model. What happens to Y as X changes by one ton according to both models?B. According
Access the file UTILITY, which contains data for the utility or satisfaction (Y) a consumer derives from the consumption of a certain good as a function of the number of units consumed (X). Graph the
A catastrophic plague has infected the citizens of Ephinacious, a small country somewhere in an obscure part of the world. Currently, 4,000 poor souls are infected and the disease is growing at the
Employees at Harvard Trust and Insurance number 1,258. Hard economic times have caused HTI to dismiss some workers at the rate of 3.5%. If less than 1,000 employees remain after three years, a bond
You currently have $43,000 at your ready disposal. An investment you plan to pursue in six years requires $60,000. If you place the $43,000 in an account paying 5.5% annually, will you have the
If the interest in problem 19 is paid continuously, will you have the $60,000?Problem 19You currently have $43,000 at your ready disposal. An investment you plan to pursue in six years requires
Monthly sales at Freeman International have been, in thousands, 45.2, 56.3, 54.8, 62.5, 74.5, 69.3, and 71.2. If the growth rate in sales exceeds 8%, the Chief Financial Officer will give himself a
The Three Brothers from Example 9.2 face per unit costs of $100 for capital and $50 for labor. They sell the product for $3.75 per unit. If they double all inputs it is felt that they will have no
A societal utility function for an entire nation is found to be In U = 3.2− 0.52lnG + 0.47 InB, where G and B are guns and butter. Interpret thecoefficients. What happens to utility for the nation
Travel expenses for Remi Electronics have been increasing at an alarming rate. In an effort to control this unfortunate trend, management has declared that if costs reach or exceed $70 thousand by
Inventory levels for Remi are currently held at $400,000 and have been increasing at a rate of 6% over the past 10 years. In order to hold down inventory costs, Remi has decided that if they exceed
If the growth rate was continuous for Remi in the previous problem, what is your conclusion?Previous problemInventory levels for Remi are currently held at $400,000 and have been increasing at a rate
Define and give examples of each of the following:A. Endogenous variables.B. Exogenous variables.C. Pre-determined variables.D. Structural equations.E. Reduced-form equations.F. Order and rank
Given these structural systems in which the Y-variables are endogenous and the X-variables are exogenous, place them in reduced form: A. Y =a+aY+Y/+X +X + E Y= Bo + BY+ BY3 + BX + BX + B5X + 2 Y= 20
Which equations are identified in each of the systems in question 2 and which are not? Explain.Question 2Given these structural systems in which the Y-variables are endogenous and the X-variables are
Clearly explain under what conditions a 2SLS model is required.Construct a system of your own making that illustrates.
Clearly explain why bias occurs in a simultaneous system. What does your response have to do with the error terms?
How do the coefficients of OLS models and those obtained from 2SLS models differ? What does this say about the bias that exists in the estimations?
In your own words thoroughly explain the identification problem and give an example.
As sales decline at Duddly Dufus Enterprises, inventories tend to reach an abnormally high level. The accompanying monthly data in hundreds of dollars record these trends. Develop and interpret the
Annual measures of output measured in thousands of tons produced for LLW Industries are shown in the accompanying table. If productivity exceeds 19 tons by 2016 the CEO of the firm will give all
Quarterly data for the number of employees and their weekly earnings are contained in the data set EARNINGS. Develop simple time series models for both employees and earnings. Discuss your findings
The Dow Jones Industrial Average is a stock market index created by Wall Street Journal and Dow Jones & Company, co-founded by Charles Dow on May 26, 1896, and now owned by Dow Jones Indexes. The
Using the data from the first problem in Section 11.1 for Duddly Dufus Enterprises, estimate an autoregressive model. Experiment with different values for p-order models until you have what you think
Using the data from the second problem in Section 11.1 for LLW Industries, estimate an autoregressive model. Experiment with different values for p-order models until you have what you think is the
Using the data from the third problem in Section 11.1 for the data set EARNINGS, estimate an autoregressive model. Experiment with different values for p-order models until you have what you think is
Using the data from the fourth problem in Section 11.1 for DOWJONES INDUSTRIALS, estimate an autoregressive model.Experiment with different values for p-order models until you have what you think is
In what way does the Koyck transformation resolve problems often associated with distributed lag models?
Given Yt = β0Xt + λYt−1, what is the short-run effect of a one-unit change in X? What is the long-run impact (multiplier) for the model?
Presume Yt = 4 + 0.73Xt + 0.291Yt−1 in a model with two lagged values. Find the coefficients for the lagged X-values.
Access the file KOYCK. Test for autocorrelation based on a Koyck model.
Discuss the differences between the Koyck and Almon lag procedures.Which do you feel is more applicable to real-world data? Why? What are the advantages and disadvantages of each?
Access the file GRANGER. The data set contains more extensive data for GNP and the money supply. Perform Granger causality tests with m = 3. Test for causality at 10% in both directions.
Under what conditions can the Granger causality be applied? What is its purpose?
In what way is the Granger test a distributed lag model?
Define and give examples of:A. Secular trend.B. Seasonal component.C. Cyclical variation.D. Irregular fluctuations.
What is the purpose of moving average and exponential smoothing?
Describe, define, and give examples of the following—detail the advantages and disadvantages of each:A. Mean Absolute Percentage Error.B. Mean Absolute Deviation.C. Mean Square Deviation.
When does a moving average fail to best perform its purpose as well as it should?
Why and when might first-differencing be necessary? What function does it perform?
Define and describe the autoregressive model. Give an example.
How many observations will you lose in the example you gave above?
An autoregressive model has 55 observations and four lagged variables. How many degrees of freedom will it have?
Define a distributed lagged model. Why is it called a distributed lagged model? Give an example.
Discuss and describe a Koyck transformation. Why is it also called a geometric lagged model? Give an example.
A variable is said to be stationary over time if it exhibits what characteristic? What restrictions does this impose on the variable's long-run mean and variance?
Define cointegration.
Discuss and describe the Almon polynomial lag. Discuss in detail how it differs from the Koyck lag.
Under what conditions can Granger causality be applied? What is its purpose? Create a complete example of your own devising, choosing carefully what variables you include in your model. Explain just
Explain how moving averages work. If the data are not stationed, what adjustments should be made?
How does single exponential smoothing work? What are its advantages compared with the moving average?

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