Econometrics Quiz: Simple Linear Regression

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Q1: A dependent variable is also known as a(n):
a) Explanatory Variable
b) Control Variable
c) Predictor Variable
d) Response Variable

Q2: In the equation Y = B1 + B2 X + u, B1 is the:
a) Dependent Variable
b) Independent Variable
c) Slope Parameter
d) Intercept Parameter

Q3: The term 'u' in the equation Y = B1 + B2 X + u is usually referred to as:
a) Sample Error or Residuals
b) Population Error or Disturbance Term

Q4: As per the method of OLS, we find the estimators of B1 and B2 such that the following is minimised:
a) The sum of residuals
b) The sum of population errors
c) The sum of squared population errors
d) The sum of squared residuals

Q5: Consider the following regression model Y = B1 + B2 X + u. Which of the following is one of the algebraic properties of OLS?
a) The sum, and therefore the sample average of OLS residuals, is positive
b) The sum of the OLS residuals is negative
c) The point (X bar, Y bar) always lies on the OLS regression line, where X bar is sample mean of X and Y bar is sample mean of Y
d) The sample covariance between the X variable and OLS residuals is positive

Q6: Consider the Simple Linear Regression Model: Y = B1 + B2 X + u.
If we estimate this model using the method of OLS, then the covariance between estimated errors (or residuals) and regressor (X) is zero by construction.
a) True
b) False

Q7: For the simple linear regression model, Y = B1 + B2 X + u , the sign (positive or negative) of the Slope estimator is the same as the sign of the Correlation between X and Y.
a) True
b) False

Q8: R2 is TSS/ESS
a) True
b) False

Q9: The value of R2 always:
a) Lies below 0
b) Lies above 1
c) Lies between 0 and 1
d) Lies between 1 and 1.5

Q10: Consider the equation, Y = B1 + B2 X + u. A null hypothesis, H0: B2 = 0 states that:
a) X has no effect on the expected value of B2
b) X has no effect on the expected value of Y
c) B2 has no effect on the expected value of Y
d) Y has no effect on the expected value of X

Q11: The general t statistic can be written as:
a) t = Hypothesized value/Standard error
b) t = estimate – hypothesized value
c) t = (estimate – hypothesized value)/variance
d) t = (estimate – hypothesized value)/standard error

Q12: Consider the following null and alternative hypotheses:
HO: B2 = 0.16
H1: B2 is greater than 0.16
The above setup:
a) indicates a one-tailed test with a rejection area in the right tail
b) indicates a one-tailed test with a rejection area in the left tail
c) indicates a two-tailed test with an acceptance region in the right tail
d) indicates a two-tailed test with a rejection area in the right tail

Q13: The error term in a regression equation is said to exhibit homoscedasticity if
a) It has zero conditional mean
b) It has the same variance for all values of the explanatory variable
c) It has the same value for all values of the explanatory variable
d) If the error term has a value of one given any value of the explanatory variable

Q14: Which of the following assumptions is not necessary for OLS estimators to be unbiased?
a) Homoscedasticity in Error term
b) Zero conditional mean of error term
c) Both the above assumptions are necessary for OLS estimators to be unbiased

Q15: Which of the following conditions is not necessary for OLS estimators to be the Best Linear Unbiased Estimators (BLUE)?
a) All errors are normally distributed
b) All errors are independent and uncorrelated to each other
c) All errors have expectation zero
d) All errors have the same variance

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