Questions and Answers of Introductory Econometrics Modern

A firm wants to bid on a contract worth $\$ 80,000$. If it spends $\$ 5000$ on the proposal it has a $50-50$ chance of getting the contract. If it spends $\$ 10,000$ on the proposal it has a
Prior to presidential elections citizens of voting age are surveyed. In the population, two characteristics of voters are their registered party affiliation (republican, democrat, or independent) and
Based on years of experience, an economics professor knows that on the first principles of economics exam of the semester $13 \%$ of students will receive an A, $22 \%$ will receive a
The LSU Tigers baseball team will play the Alabama baseball team in a weekend series of two games. Let $W=0,1$, or 2 equal the number of games LSU wins. Let the weekend's weather be designated as
A clinic specializes in shoulder injuries. A patient is randomly selected from the population of all clinic clients. Let $S$ be the number of doctor visits for shoulder problems in the past six
As you walk into your econometrics exam, a friend bets you $\$ 20$ that she will outscore you on the exam. Let $X$ be a random variable denoting your winnings. $X$ can take the values 20, 0 [if
Breast cancer prevalence in the United Kingdom can be summarized for the population (data are in 1000s) as in Table P. 12.a. Compute the probability that a randomly drawn person has breast cancer.b.
A continuous random variable $Y$ has $p d f$a. Sketch the $p d f$.b. Find the $c d f, F(y)=P(Y \leq y)$ and sketch it. c. Use the $p d f$ and a geometric argument to find the probability
Answer each of the following:a. An internal revenue service auditor knows that $3 \%$ of all income tax forms contain errors. Returns are assigned randomly to auditors for review. What is the
Let $X$ and $Y$ be random variables with expected values $\mu=\mu_{X}=\mu_{Y}$ and variances $\sigma^{2}=\sigma_{X}^{2}=\sigma_{Y}^{2}$. Let $Z=(2 X+Y) / 2$.a. Find the expected value of
Suppose the $p d f$ of the continuous random variable $X$ is $f(x)=1$, for \(0
A fair die is rolled. Let $Y$ be the face value showing, 1, 2, 3, 4, 5, or 6 with each having the probability $1 / 6$ of occurring. Let $X$ be another random variable that is given bya. Find
A large survey of married women asked "How many extramarital affairs did you have last year?" $77 \%$ said they had none, $5 \%$ said they had one, $2 \%$ said two, $3 \%$ said three, and the
Let NKIDS represent the number of children ever born to a woman. The possible values of NKIDS are $n k i d s=0,1,2,3,4, \ldots$ Suppose the $p d f$ is \(f(n k i d s)=2^{\text {nkids }} /(7.389 n
Five baseballs are thrown to a batter who attempts to hit the ball 350 feet or more. Let $H$ denote the number of successes, with the $p d$ for having $h$ successes being \(f(h)=120 \times
An author knows that a certain number of typographical errors $(0,1,2,3, \ldots)$ are on each book page. Define the random variable $T$ equaling the number of errors per page. Suppose that $T$
Explain the difference between a random variable and its values, and give an example.
Explain the difference between discrete and continuous random variables, and give examples of each.
State the characteristics of a probability density function ( $p d f$ ) for a discrete random variable, and give an example.
Compute probabilities of events, given a discrete probability function.
Explain the meaning of the following statement: "The probability that the discrete random variable takes the value 2 is 0.3 ."
Explain how the $p d f$ of a continuous random variable is different from the $p d f$ of a discrete random variable.
Show, geometrically, how to compute probabilities given a $p d f$ for a continuous random variable.
Explain, intuitively, the concept of the mean, or expected value, of a random variable.
Use the definition of expected value for a discrete random variable to compute expectations, given a $p d f f(x)$ and a function $g(X)$ of $X$.
Define the variance of a discrete random variable, and explain in what sense the values of a random variable are more spread out if the variance is larger.
Use a joint $p d f$ (table) for two discrete random variables to compute probabilities of joint events and to find the (marginal) pdf of each individual random variable.Data From Table:- TABLE P.3
Find the conditional $p d f$ for one discrete random variable given the value of another and their joint $p d f$.
Give an intuitive explanation of statistical independence of two random variables, and state the conditions that must hold to prove statistical independence. Give examples of two independent random
Define the covariance and correlation between two random variables, and compute these values given a joint probability function of two discrete random variables.
Find the mean and variance of a sum of random variables.
Use the Law of Iterated Expectations to find the expected value of a random variable.
Explain the difference between an estimator and an estimate, and why the least squares estimators are random variables, and why least squares estimates are not.
Discuss the interpretation of the slope and intercept parameters of the simple regression model, and sketch the graph of an estimated equation.
Explain the theoretical decomposition of an observable variable $y$ into its systematic and random components, and show this decomposition graphically.
Explain how the least squares principle is used to fit a line through a scatter plot of data. Be able to define the least squares residual and the least squares fitted value of the dependent variable
Define the elasticity of $y$ with respect to $x$ and explain its computation in the simple linear regression model when $y$ and $x$ are not transformed in any way, and when $y$ and/or $x$
Explain the meaning of the statement "If regression model assumptions SR1-SR5 hold, then the least squares estimator $b_{2}$ is unbiased." In particular, what exactly does "unbiased" mean? Why is
Explain the meaning of the phrase "sampling variability."
Explain how the factors $\sigma^{2}, \Sigma\left(x_{i}-\bar{x}\right)^{2}$, and $N$ affect the precision with which we can estimate the unknown parameter $\beta_{2}$.
State and explain the Gauss-Markov theorem.Data From Gauss-Markov Theorem:- 2.5 The Gauss-Markov Theorem What can we say about the least squares estimators b and b so far? The estimators are
Use the least squares estimator to estimate nonlinear relationships and interpret the results.
Explain the difference between an explanatory variable that is fixed in repeated samples and an explanatory variable that is random.
Explain the term "random sampling."
Consider the following five observations. You are to do all the parts of this exercise using only a calculator.a. Complete the entries in the table. Put the sums in the last row. What are the sample
A household has weekly income of $\$ 2000$. The mean weekly expenditure for households with this income is $E(y \mid x=\$ 2000)=\mu_{y \mid x=\$ 2000}=\$ 220$, and expenditures exhibit variance
Graph the following observations of $x$ and $y$ on graph paper.a. Using a ruler, draw a line that fits through the data. Measure the slope and intercept of the line you have drawn.b. Use formulas
We have defined the simple linear regression model to be $y=\beta_{1}+\beta_{2} x+e$. Suppose, however, that we knew, for a fact, that $\beta_{1}=0$.a. What does the linear regression model look
A small business hires a consultant to predict the value of weekly sales of their product if their weekly advertising is increased to $\$ 2000$ per week. The consultant takes a record of how much
A soda vendor at Louisiana State University football games observes that the warmer the temperature at game time the greater the number of sodas that are sold. Based on 32 home games covering five
We have 2008 data on $y=$ income per capita (in thousands of dollars) and $x=$ percentage of the population with a bachelor's degree or more for the 50 U.S. states plus the District of Columbia,
Professor I.M. Mean likes to use averages. When fitting a regression model $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$ using the $N=6$ observations in Table 2.4 from Exercise 2.3, \(\left(y_{i},
Professor I.M. Mean likes to use averages. When fitting a regression model $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$ using the $N=6$ observations in Table 2.4 from Exercise 2.3, \(\left(y_{i},
Consider fitting a regression model $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$ using the $N=6$ observations in Table 2.4 from Exercise 2.3, $\left(y_{i}, x_{i}\right)$. Suppose that based on a
Let $y=$ expenditure ( $\$$ ) on food away from home per household member per month in the past quarter and $x=$ monthly household income (in hundreds of dollars) during the past year.a. Using
Let $y=$ expenditure ( $\$$ ) on food away from home per household member per month in the past quarter and $x=1$ if the household includes a member with an advanced degree, a Master's, or
Using 2011 data on 141 U.S. public research universities, we examine the relationship between academic cost per student, $A C A$ (real total academic cost per student in thousands of dollars) and
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 and $E D U C$ is years of education, or schooling. The regression
Professor E.Z. Stuff has decided that the least squares estimator is too much trouble. Noting that two points determine a line, Dr. Stuff chooses two points from a sample of size $N$ and draws a
The capital asset pricing model (CAPM) is an important model in the field of finance. It explains variations in the rate of return on a security as a function of the rate of return on a portfolio
The data file collegetown contains observations on 500 single-family houses sold in Baton Rouge, Louisiana, during 2009-2013. The data include sale price (in thousands of dollars), PRICE, and total
The data file collegetown contains observations on 500 single-family houses sold in Baton Rouge, Louisiana, during 2009-2013. The data include sale price (in thousands of dollars), PRICE, and total
The data file stockton5_small contains observations on 1200 houses sold in Stockton, California, during 1996-1998. [Note: the data file stockton5 includes 2610 observations.] Scale the variable
The data file stockton5_small contains observations on 1200 houses sold in Stockton, California, during 1996-1998. [Note: The data file stockton5 includes 2610 observations.]. Scale the variable
The data file stockton5_small contains observations on 1200 houses sold in Stockton, California, during 1996-1998. [Note: the data file stockton5 includes 2610 observations.] Scale the variable
A longitudinal experiment was conducted in Tennessee beginning in 1985 and ending in 1989. A single cohort of students was followed from kindergarten through third grade. In the experiment children
Professor Ray C. Fair has for a number of years built and updated models that explain and predict the U.S. presidential elections. Visit his website at
Using data on the "Ashcan School"14 we have an opportunity to study the market for art. What factors determine the value of a work of art? Use the data in ashcan_small. For this exercise, use data
Consumer expenditure data from 2013 are contained in the file cex5_small. [Note: cex5 is a larger version with more observations and variables.] Data are on three-person households consisting of a
Consumer expenditure data from 2013 are contained in the file cex5_small. [Note: cex5 is a larger version with more observations and variables.] Data are on three-person households consisting of a
The owners of a motel discovered that a defective product was used in its construction. It took seven months to correct the defects during which 14 rooms in the 100-unit motel were taken out of
How much does education affect wage rates? The data file cps5_small contains 1200 observations on hourly wage rates, education, and other variables from the 2013 Current Population Survey (CPS). a.
How much does education affect wage rates? The data file cps5_small contains 1200 observations on hourly wage rates, education, and other variables from the 2013 Current Population Survey (CPS). a.
In this exercise, we consider the amounts that are borrowed for single family home purchases in Las Vegas, Nevada, during 2010. Use the data file vegas5_small for this exercise.a. Compute summary
Discuss how "sampling theory" relates to interval estimation and hypothesis testing.
Explain why it is important for statistical inference that given $\mathbf{x}$ the least squares estimators $b_{1}$ and $b_{2}$ are normally distributed random variables.
Explain the "level of confidence" of an interval estimator, and exactly what it means in a sampling context, and give an example.
Explain the difference between an interval estimator and an interval estimate. Explain how to interpret an interval estimate.
Explain the terms null hypothesis, alternative hypothesis, and rejection region, giving an example and a sketch of the rejection region.
Explain the logic of a statistical test, including why it is important that a test statistic has a known probability distribution if the null hypothesis is true.
Explain the term $p$-value and how to use a $p$-value to determine the outcome of a hypothesis test; provide a sketch showing a $p$-value.
Explain the difference between one-tail and two-tail tests. Explain, intuitively, how to choose the rejection region for a one-tail test.
Explain Type I error and illustrate it in a sketch. Define the level of significance of a test.
Explain the difference between economic and statistical significance.
Explain how to choose what goes in the null hypothesis and what goes in the alternative hypothesis.
There were 64 countries in 1992 that competed in the Olympics and won at least one medal. Let MEDALS be the total number of medals won, and let GDPB be GDP (billions of 1995 dollars). A linear
There were 64 countries in 1992 that competed in the Olympics and won at least one medal. Let MEDALS be the total number of medals won, and let GDPB be GDP (billions of 1995 dollars). A linear
There were 64 countries in 1992 that competed in the Olympics and won at least one medal. Let MEDALS be the total number of medals won, and let GDPB be GDP (billions of 1995 dollars). A linear
Assume that assumptions SR1-SR6 hold for the simple linear regression model, $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$, $i=1, \ldots, N$. Generally, as the sample size $N$ becomes larger,
If we have a large sample of data, then using critical values from the standard normal distribution for constructing a $\boldsymbol{p}$-value is justified. But how large is "large"?a. For a
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
We have 2008 data on INCOME = income per capita (in thousands of dollars) and BACHELOR = percentage of the population with a bachelor's degree or more for the 50 U.S. States plus the District of
Using 2011 data on 141 U.S. public research universities, we examine the relationship between cost per student and full-time university enrollment. Let $A C A=$ real academic cost per student
Using data from 2013 on 64 black females, the estimated linear regression between WAGE (earnings per hour, in \$) and years of education, EDUC is $\widehat{W A G E}=-8.45+1.99 E D U C$.a. The
Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earnings per hour, in \$) and years of education, EDUC is $\widehat{\ln (W A G E)}=1.58+0.09 E D U C$.
The theory of labor supply indicates that more labor services will be offered at higher wages. Suppose that HRSWK is the usual number of hours worked per week by a randomly selected person and WAGE
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 following estimated area response model for sugar cane (area of sugar cane planted in thousands of hectares in a region of Bangladesh), as a function of relative price (100 times the
What is the meaning of statistical significance and how valuable is this concept? A $t$-statistic is $t=(b-c) / \operatorname{se}(b)$, where $b$ is an estimate of a parameter $\beta, c$ is
In a capital murder trial, with a potential penalty of life in prison, would you as judge tell the jury to make sure that we accidently convict an innocent person only one time in a hundred, or use

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