Question 1

If we use as an estimator of $\sigma$² it is _______________,but it can be corrected by _______________. A)biased,changing the numerator to B)non-linear,changing the denominator to N - 2 C)biased,changing the denominator to N-2 D)non-linear,taking the log of each term.

Accepted Answer

biased,changing the denominator to N-2&#10;

Question 2

In an economic model that uses income to predict monthly expenditures on entertainment,what is the dependent variable?&#10;A)income&#10;B)monthly expenditures on entertainment&#10;C)income elasticity&#10;D)demand for entertainment

Accepted Answer

The dependent variable is the one that is being predicted or affected by the independent variable, which in this case is income. Therefore, the dependent variable in this economic model is the monthly expenditures on entertainment.

Question 3

How do you interpret the estimated value of $\gamma$ ₂ in the following equation: ln(ENT_EXP)= $\gamma$ ₁ + $\gamma$ ₂ (INCOME)+ e
Where INCOME is annual household income (in thousands)and ENT_EXP is annual entertainment expenses?

A)the income elasticity of entertainment
B). )when multiplied by 100 it is the percentage increase in entertainment expenses associated with an additional $1000 in income
C)the increase in entertain expenses associated with a 1% increase in income
D)the average of the logarithm of entertainment expenses for a household with zero income

. )when multiplied by 100 it is the percentage increase in entertainment expenses associated with an additional $1000 in income

Accepted Answer

The estimated value of F1F1F1S1F1F1F10₂ in the equation represents the increase in entertainment expenses associated with a $1000 increase in income, when multiplied by 100. This is because the coefficient of INCOME is given as 1000 times the estimated value of F1F1F1S1F1F1F10₁ and the exponential function on the left side of the equation implies a logarithmic relationship between ENT_EXP and the predictors. Therefore, Choice B is the best answer.

Question 4

Applying the OLS model to our data give us the following regression equation: ŷ = 3.41 + 12.89 x.
What would the forecast value be when the independent variable is 15.0?

A)196.76
B)16.30
C)244.50
D)32.19

Accepted Answer

To forecast the value when the independent variable is 15.0, substitute x = 15.0 into the regression equation: ŷ = 3.41 + 12.89(15.0) = 3.41 + 193.35 = 196.76.

Question 5

The OLS estimators for $\beta$₁and$\beta$₂are formulas derived by minimizing _____________. A)the sum of the error terms or residuals B)the sum of the squared residuals C)the slope of the regression line D)the fit of the regression line to the observed data.

Accepted Answer

The OLS estimators are derived by minimizing the sum of the squared residuals, which is also known as the residual sum of squares (RSS). This is because the RSS measures the distance between the observed data points and the predicted values from the regression line, and the goal is to minimize this distance to obtain the best fit line.

Question 6

In the OLS model,what happens to var(b₁)as the sample size (N)increases? A)it also increases B)it decreases C)it does not change D)cannot be determined without more information

Accepted Answer

As the sample size increases, the standard error of the slope coefficient (b) decreases, leading to decreased variance of the product of b, S1, U1, B1, and B0. Therefore, option B is the best choice as variance decreases.

Question 7

How do you interpret the estimated value of $\gamma$ ₂ in the following equation: ln(ENT_EXP)= $\gamma$ ₁ + $\gamma$ ₂ (INCOME)+ e
Where INCOME is annual household income (in thousands)and ENT_EXP is annual entertainment expenses?

A)the income elasticity of entertainment
B). )when multiplied by 100 it is the percentage increase in entertainment expenses associated with an additional $1000 in income
C)the increase in entertain expenses associated with a 1% increase in income
D)the average of the logarithm of entertainment expenses for a household with zero income

. )when multiplied by 100 it is the percentage increase in entertainment expenses associated with an additional $1000 in income

Accepted Answer

The estimated value of F1F1F1S1uf067F1F1F10₁ in the equation represents the intercept term in a log-linear model, which corresponds to the average of the logarithm of entertainment expenses when INCOME is zero.

Question 8

Which of the following non-linear adjustments CANNOT be accommodated using OLS?&#10;A)including an independent variable that has been raised to a power&#10;B)taking a logarithmic transformation of the dependent variable&#10;C)including a binary indicator variable&#10;D)raising parameters to a power

Accepted Answer

OLS can accommodate non-linear transformations of independent variables (option A) and dependent variables (option B) as well as binary indicator variables (option C), but it cannot handle raising parameters to a power (option D). This is because OLS assumes a linear relationship between the dependent and independent variables and raising parameters to a power would violate this assumption. Non-linear regressions, such as polynomial or exponential regressions, would need to be used instead.

Question 9

Under the Gauss-Markov Theorem when assumptions SR1 - SR5 are met,what estimators of $\beta$₁ and $\beta$₂ may have smaller variances than b₁ and b₂? A)none B)a non-linear estimator C)a normally distributed estimator D)an estimator derived from economic theory

Accepted Answer

The answer of Under the Gauss-Markov Theorem when assumptions SR1...

Question 10

Which of the following is NOT an assumption of the Simple Linear Regression Model? A)The value of y,for each value of x,is y = $\beta$₁ +$\beta$₂x + e B)The variance of the random error e is var(e)= $\sigma$² C)The covariance between any pair of random errors e_i and e_j is zero D)The parameter estimate of $\beta$₁is unbiased.

Accepted Answer

The assumption D, regarding the parameter estimate being unbiased, is not an assumption of the Simple Linear Regression Model itself but a property of the estimators under certain conditions.

Question 11

You have estimated the following equation using OLS: ŷ = 33.75 + 1.45 MALE
Where y is annual income in thousands and MALE is an indicator variable such that it is 1 for males and 0 for females.According to this model,what is the average income for females?

A)$33,750
B)$35,200
C)$32,300
D)cannot be determined

Accepted Answer

The answer of You have estimated the following equation using...

Question 12

In an economic model that uses income to predict monthly expenditures on entertainment,what is the independent or explanatory variable?&#10;A)income&#10;B)monthly expenditures on entertainment&#10;C)income elasticity&#10;D)demand for entertainment

Accepted Answer

The answer of In an economic model that uses income...

Question 13

If b₁is an estimator for $\beta$₁such that E(b₁)=$\beta$₁ ,then it must be the case that A)b₁is an efficient estimator B)b₁is an unbiased estimator C)b₁is a linear estimator D)b₁is a preferred estimator

Accepted Answer

The answer of If b₁is an estimator for $\beta$₁_...

Question 14

What mathematical theorem allows for normally distributed least squares estimators when assumptions SR1 - SR5 hold but the error term is NOT normally distributed?&#10;A)Central Limit Theorem&#10;B)Gauss-Markov Theorem&#10;C)Law of Large Numbers&#10;D)the Least Squares Principle

Accepted Answer

The answer of What mathematical theorem allows for normally distributed...

Question 15

You have estimated the following equation using OLS: ŷ = 33.75 + 1.45 MALE
Where y is annual income in thousands and MALE is an indicator variable such that it is 1 for males and 0 for females.According to this model,what is the average income for females?

A)$33,750
B)$35,200
C)$32,300
D)cannot be determined

Accepted Answer

The answer of You have estimated the following equation using...

Deck 3: The Simple Linear Regression Model