Questions and Answers of Introductory Econometrics Modern

Test the overall significance of a regression model and identify the components of this test from your computer output.
Explain the concepts of restricted and unrestricted sums of squared errors and how they are used to test hypotheses.
Use the $F$-test to test single null hypotheses or joint null hypotheses.
Use your computer software to perform an $F$-test.
From output of your computer software, locate (a) the sum of squared errors, (b) the $F$-value for the overall significance of a regression model, (c) the estimated covariance matrix for the least
Explain the relationship between the finite sample $F$-test and the large sample $\chi^{2}$-test, and the assumptions under which each is suitable.
Obtain restricted least squares estimates that include nonsample information in the estimation procedure.
Explain the properties of the restricted least squares estimator. In particular, how do its bias and variance compare with those of the unrestricted, ordinary, least squares estimator?
Explain the differences between models designed for prediction and models designed to estimate a causal effect.
Explain what is meant by (a) an omitted variable and (b) an irrelevant variable. Explain the consequences of omitted and irrelevant variables for the properties of the least squares estimator.
Explain the concept of a control variable and the assumption necessary for a control variable to be effective.
Explain the issues that need to be considered when choosing a regression model.
Compute forecasts, standard errors of forecast errors, and interval forecasts from a multiple regression model.
Use the Akaike information or Schwartz criteria to select variables for a predictive model.
Identify collinearity and explain its consequences for least squares estimation.
Identify influential observations in a multiple regression model.
Compute parameter estimates for a regression model that is nonlinear in the parameters and explain how nonlinear least squares differs from linear least squares.
Answer each of the following:a. Suppose that a simple regression has quantities $N=20, \Sigma y_{i}^{2}=7825.94, \bar{y}=19.21$, and $S S R=375.47$, find $R^{2}$.b. Suppose that a simple
Consider the following estimated regression equation (standard errors in parentheses):Rewrite the estimated equation, including coefficients, standard errors, and $R^{2}$, that would result ifa.
We have five observations on $x$ and $y$. They are $x_{i}=3,2,1,-1,0$ with corresponding $y$ values $y_{i}=4,2,3,1,0$. The fitted least squares line is $\hat{y}_{i}=1.2+0.8 x_{i}$, the
The general manager of a large engineering firm wants to know whether the experience of technical artists influences their work quality. A random sample of 50 artists is selected. Using years of work
Consider the regression model $W A G E=\beta_{1}+\beta_{2} E D U C+e$. WAGE is hourly wage rate in U.S. 2013 dollars. $E D U C$ is years of education attainment, or schooling. The model is
We have five observations on $x$ and $y$. They are $x_{i}=3,2,1,-1,0$ with corresponding $y$ values $y_{i}=4,2,3,1,0$. The fitted least squares line is $\hat{y}_{i}=1.2+0.8 x_{i}$, the
We have data on 2323 randomly selected households consisting of three persons in 2013. Let ENTERT denote the monthly entertainment expenditure (\$) per person per month and let INCOME $$100$ be
Consider a log-linear regression for the weekly sales (number of cans) of a national brand of canned tuna $(S A L 1=$ target brand sales $)$ as a function of the ratio of its price to the price
Consider the weekly sales (number of cans) of a national brand of canned tuna (SAL1 = target brand sales) as a function of the ratio of its price to the price of a competitor, RPRICE3 = 100 (price of
Using data on 76 countries, we estimate a relationship between the growth rate in prices, INFLAT, and the rate of growth in the money supply, MONEY. The least squares estimates of the model are as
Consider the regression model $W A G E=\beta_{1}+\beta_{2} E D U C+e$ where $W A G E$ is hourly wage rate in U.S. 2013 dollars, $E D U C$ is years of education attainment. The model is
Consider the share of total household expenditure (TOTEXP) devoted to expenditure on food (FOOD). Specify the log-linear relationship FOOD/TOTEXP $=\beta_{1}+\beta_{2} \ln ($ TOTEXP $)$.a. Show
The linear regression model is $y=\beta_{1}+\beta_{2} x+e$. Let $\bar{y}$ be the sample mean of the $y$-values and $\bar{x}$ the average of the $x$-values. Create variables
Using data on 5766 primary school children, we estimate two models relating their performance on a math test (MATHSCORE) to their teacher's years of experience (TCHEXPER).a. Using the linear fitted
Consider a log-reciprocal model that relates the logarithm of the dependent variable to the reciprocal of the explanatory variable, $\ln (y)=\beta_{1}+\beta_{2}(1 / x)$.a. For what values of $y$
In Section 4.6, we considered the demand for edible chicken, which the U.S. Department of Agriculture calls "broilers." The data for this exercise are in the file newbroiler.a. Using the 52 annual
McCarthy and Ryan (1976) considered a model of television ownership in the United Kingdom and Ireland using data from 1955 to 1973 . Use the data file $t v d a t a$ for this exercise.a. For the
Do larger universities have lower cost per student or a higher cost per student? Use the data on 141 public universities in the data file pubcoll for 2010 and 2011. A university is many things and
The data file wa_wheat contains wheat yield for several shires in Western Australia from 1950 to 1997.a. If the variable YIELD is "average wheat yield" in tonnes per hectare what is the
In the log-linear model $\ln (y)=\beta_{1}+\beta_{2} x+e$, the corrected predictor $\hat{y}_{c}=\exp \left(b_{1}+b_{2} x\right) \times \exp \left(\hat{\sigma}^{2} / 2\right)$ is argued to have a
The data file malawi_small contains survey data from Malawi during 2007-2008 on total household expenditures in the prior month (in Malawian Kwacha) as well as expenditures on categories of goods
The data file malawi_small contains survey data from Malawi during 2007-2008 on total household expenditures in the prior month (in Malawian Kwacha) as well as expenditures on categories of goods
The data file malawi_small contains survey data from Malawi during 2007-2008 on total household expenditures in the prior month (in Malawian Kwacha) as well as expenditures on categories of goods
Reconsider the presidential voting data (fair5) introduced in Exercises 2.23 and 3.24.a. Using all the data from 1916 to 2012 , estimate the regression model VOTE \(=\beta_{1}+\beta_{2} G R O W T
The file collegetown contains data on 500 houses sold in Baton Rouge, LA during 2009-2013. Variable descriptions are in the file collegetown.def.a. Estimate the log-linear model \(\ln (P R I C
The file collegetown contains data on 500 houses sold in Baton Rouge, LA during 2009-2013. Variable descriptions are in the file collegetown.def.a. Estimate the log-linear model \(\ln (P R I C
Does the return to education differ by race and gender? For this exercise use the file cps5. [This is a large file with 9799 observations. If your software is a student version, you can use the
The file wa-wheat.dat contains observations on wheat yield in Western Australian shires. There are 48 annual observations for the years 1950-1997. For the Northampton shire, consider the following
Consider a model for household expenditure as a function of household income using the 2013 data from the Consumer Expenditure Survey, cex5_small. The data file cex5 contains more observations. Our
Consider a model for household expenditure as a function of household income using the 2013 data from the Consumer Expenditure Survey, cex5_small. The data file cex5 contains more observations. Our
Recognize a multiple regression model and be able to interpret the coefficients in that model.
Understand and explain the meanings of the assumptions for the multiple regression model.
Use your computer to find least squares estimates of the coefficients in a multiple regression model, and interpret those estimates.
Explain the meaning of the Gauss-Markov theorem.
Compute and explain the meaning of $R^{2}$ in a multiple regression model.
Explain the Frisch-Waugh-Lovell Theorem and estimate examples to show how it works.
Use your computer to obtain variance and covariance estimates, and standard errors, for the estimated coefficients in a multiple regression model.
Explain the circumstances under which coefficient variances (and standard errors) are likely to be relatively high, and those under which they are likely to be relatively low.
Find interval estimates for single coefficients and linear combinations of coefficients, and interpret the interval estimates.
Test hypotheses about single coefficients and about linear combinations of coefficients in a multiple regression model. In particular,a. What is the difference between a one-tail and a two-tail
Estimate and interpret multiple regression models with polynomial and interaction variables.
Find point and interval estimates and test hypotheses for marginal effects in polynomial regressions and models with interaction variables.
Explain the difference between finite and large sample properties of an estimator.
Explain what is meant by consistency and asymptotic normality.
Consider the multiple regression modelwith the seven observations on $y_{i}, x_{i 1}, x_{i 2}$, and $x_{i 3}$ given in Table 5.5.Use a hand calculator or spreadsheet to answer the following
Use your answers to Exercise 5.1 toa. Compute a $95 \%$ interval estimate for $\beta_{2}$.b. Test the hypothesis $H_{0}: \beta_{2}=1.25$ against the alternative that \(H_{1}: \beta_{2} eq
Consider the following model that relates the percentage of a household's budget spent on alcohol WALC to total expenditure TOTEXP, age of the household head $A G E$, and the number of children in
Consider the following model that relates the percentage of a household's budget spent on alcohol, $W A L C$, to total expenditure TOTEXP, age of the household head $A G E$, and the number of
For each of the following two time-series regression models, and assuming MR1-MR6 hold, find $\operatorname{var}\left(b_{2} \mid \mathbf{x}\right)$ and examine whether the least squares estimator
Suppose that, from a sample of 63 observations, the least squares estimates and the corresponding estimated covariance matrix are given byUsing a 5\% significance level, and an alternative hypothesis
After estimating the model $y=\beta_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+e$ with $N=203$ observations, we obtain the following information: \(\sum_{i=1}^{N}\left(x_{i
There were 79 countries who competed in the 1996 Olympics and won at least one medal. For each of these countries, let MEDALS be the total number of medals won, POPM be population in millions, and
There were 64 countries who competed in the 1992 Olympics and won at least one medal. For each of these countries, let MEDALS be the total number of medals won, $P O P M$ be population in millions,
Using data from 1950 to 1996 ( $T=47$ observations), the following equation for explaining wheat yield in the Mullewa Shire of Western Australia was estimated aswhere $Y I E L D_{t}=$ wheat yield
When estimating wage equations, we expect that young, inexperienced workers will have relatively low wages; with additional experience their wages will rise, but then begin to decline after middle
This exercise uses data on 850 houses sold in Baton Rouge, Louisiana during mid-2005. We will be concerned with the selling price in thousands of dollars (PRICE), the size of the house in hundreds of
A concept used in macroeconomics is Okun's Law, which states that the change in unemployment from one period to the next depends on the rate of growth of the economy relative to a "normal" growth
Consider the regression model $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$ where the pairs $\left(y_{i}, x_{i}\right), i=1,2, \ldots, N$, are random independent draws from a population.a. Suppose the
Consider the regression model $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$ where the pairs $\left(y_{i}, x_{i}\right), i=1,2, \ldots, N$, are random independent draws from a population, \(x_{i} \sim
Consider a log-linear regression for the weekly sales of a national brand of canned tuna (brand $A$ ), expressed as thousands of cans, CANS, as a function of the prices of two competing brands
Use econometric software to verify your answers to Exercise 5.1, parts (c), (e), (f), (g), and (h).Data From Exercise 5.1:-Consider the multiple regression modelwith the seven observations on
Consider the following two expenditure share equations where the budget share for food WFOOD, and the budget share for clothing WCLOTH, are expressed as functions of total expenditure TOTEXP.a. A
Consider the following expenditure share equation where the budget share for food WFOOD is expressed as a function of total expenditure TOTEXP.In Exercise 4.12, it was noted that the elasticity of
A generalized version of the estimator for $\beta_{2}$ proposed by Professor I.M. Mean for the regression model $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}, i=1,2, \ldots, N$ iswhere
Using the data in the file toody 5 , estimate the modelwhere $Y_{t}=$ wheat yield in tons per hectare in the Toodyay Shire of Western Australia in year $t$; $T R E N D_{t}$ is a trend variable
Using the data in the file toody 5 , estimate the modelwhere $Y_{t}=$ wheat yield in tons per hectare in the Toodyay Shire of Western Australia in year $t$; $T R E N D_{t}$ is a trend variable
The file cocaine contains 56 observations on variables related to sales of cocaine powder in northeastern California over the period 1984-1991. The data are a subset of those used in the study
The file collegetown contains data on 500 single-family houses sold in Baton Rouge, Louisiana during 2009-2013. We will be concerned with the selling price in thousands of dollars (PRICE), the size
The file collegetown contains data on 500 single-family houses sold in Baton Rouge, Louisiana during 2009-2013. We will be concerned with the selling price in thousands of dollars (PRICE), and the
Consider the presidential voting data (data file fair5) introduced in Exercise 2.23. Details of the variables can be found in that exercise.a. Using all observations, estimate the regression
In this exercise, we consider the auction market for art first introduced in Exercise 2.24. The variables in the data file ashcan_small that we will be concerned with are as follows:RHAMMER $=$ the
In this exercise, we consider the auction market for art first introduced in Exercise 2.24. The variables in the data file ashcan_small that we will be concerned with are as follows:Create a new
What is the relationship between crime and punishment? This important question has been examined by Cornwell and Trumbull ${ }^{16}$ using a panel of data from North Carolina. The cross sections
In Section 5.7.4, we discovered that the optimal level of advertising for Big Andy's Burger Barn, $A D V E R T_{0}$, satisfies the equation $\beta_{3}+2 \beta_{4} A D V E R T_{0}=1$. Using a \(5
Each morning between 6:30 AM and 8:00 AM Bill leaves the Melbourne suburb of Carnegie to drive to work at the University of Melbourne. The time it takes Bill to drive to work (TIME), depends on the
Reconsider the variables and model from Exercise 5.31Suppose that Bill is mainly interested in the magnitude of the coefficient $\beta_{2}$. He has control over his departure time, but no control
Use the observations in the data file cps5_small to estimate the following model:a. At what levels of significance are each of the coefficient estimates "significantly different from zero"?b. Obtain
Let $x_{1}=17, x_{2}=1, x_{3}=0 ; y_{1}=5, y_{2}=2, y_{3}=8$. Calculate the following:a. $\sum_{i=1}^{2} x_{i}$b. $\sum_{t=1}^{3} x_{t} y_{t}$c. \(\bar{x}=\left(\sum_{i=1}^{3} x_{i}\right) /
Express each of the following sums in summation notation.a. $\left(x_{1} / y_{1}\right)+\left(x_{2} / y_{2}\right)+\left(x_{3} / y_{3}\right)+\left(x_{4} / y_{4}\right)$b. $y_{2}+y_{3}+y_{4}$c.
Write out each of the following sums and compute where possible.a. $\sum_{i=1}^{3}\left(a-b x_{i}\right)$b. $\sum_{t=1}^{4} t^{2}$c. $\sum_{x=0}^{2}\left(2 x^{2}+3 x+1\right)$d.
Show algebraically thata. $\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}=\left(\sum_{i=1}^{n} x_{i}^{2}\right)-n \bar{x}^{2}$b.
Let SALES denote the monthly sales at a bookstore. Assume SALES are normally distributed with a mean of $\$ 50,000$ and a standard deviation of $\$ 6000$.a. Compute the probability that the firm
A venture capital company feels that the rate of return $(X)$ on a proposed investment is approximately normally distributed with a mean of $40 \%$ and a standard deviation of $10 \%$.a. Find

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