Reference no: EM132368510

Questions -

Q1. Which of the following is NOT an assumption of the multiple regression model?

a) The value of y, for each value of x_ik, is: y_i = β₁ + β₂x_i2 + ... + β_Kx_iK + e_i

b) The value of y, for each value of x, is: y = β₁ + β₂x + e

c) Cov(e_i , e_j) = 0 , i ≠ j

d) E(e) = 0.

Q2. You have estimated a model of two variables related such that

y = 16.8 - 20 x

If x increases by 1 unit, what is the expected change in y?

a) y decreases by 0.2 percent

b) y decreases by 0.2 units.

c) y decreases by 2 percent.

d) y decreases by 20 units.

Q3. A model estimated using a dataset with 500 observations generates the following results.

y = 3.204 + 0.76 x₂

(se) (0.709) (0.44)

What are the endpoints for the 99% confidence interval for β₂?

Percentiles of the t-distribution: t_(.95,df) = 1.645, t_(.975,df) = 1.96, t_(.99,df) = 2.326, t_(.995,df) =2.576

a) (1.5549, 4.8531)

b) (1.3776, 5.0304)

c) (-0.2634, 1.7834)

d) (-0.3734, 1.8934)

Q4. How should b_k in the general multiple regression model be interpreted?

a) the number of variables used in the model.

b) the magnitude of variance caused by x_k in the model.

c) the number of units of change in the expected value of y for a 1 unit increase in x_k when all remaining variables are unchanged.

d) the amount of variation in errors caused by x_k in the model when all remaining variables are unchanged.

Q5. You have estimated the following equation using OLS:

y = 33.75 + 1.45 EDU

where y is annual income in thousands and EDU is the year of education. According to this model, what is the marginal income for an additional year of education?

a) $1,450

b) $3,375

c) $3,520

d) $33,750

Q6. You have estimated the following equation using OLS:

y = 33.75 + 1.2 EDU + 0.5 EDU x EXPER

where y is annual income in thousands, EDU is the year of education, and EXPER is the year of work experience. According to this model, what is the marginal income for an additional year of education when the work experience is 2 years?

a) $1,200

b) $1,700

c) $2,200

d) $3,625

Q7. Which of the following is correct?

a) R² measures the standard deviation of the error term.

b) If R² = 0, then the model fits the data perfectly.

c) The closer R² is to 1, the closer the sample values yi are to the fitted regression equation.

d) If the sample data for y and x are uncorrelated, R² = 1.

Q8. Which of the following is correct about the least squares method?

a) The least squares estimators are the best linear unbiased estimators when the assumptions SR1-SR5 are satisfied.

b) The least squares estimator are obtained by maximizing the sum of squared errors.

c) If the assumptions are held, R² = 1.

d) If the sample data for y and x are uncorrelated, the least squares estimators are the linear unbiased estimators.

Q9. Under the assumptions SR1-SR5 of the linear regression model, Gauss-Markov Theorem says,

a) the estimators b₁ and b₂ are biased.

b) the estimators b₁ and b₂ have the largest variance of all estimator.

c) the estimators b₁ and b₂ are the best linear unbiased estimators of b₁ and b₂.

d) the estimators b₁ and b₂ are the Best non-linear unbiased estimators of b₁ and b₂.

Q10. You estimate a simple linear regression model using a sample of 27 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 67.52 + 19.74 x

(3.12) (3.42)

What are the endpoints of the interval estimator for β₂ with a 95% interval estimate? Percentile of the t-distribution:

df	t(.90,df)	t(.95,df)	t(.975,df)	t(.99,df)	t(.995,df)
25	1.316	1.708	2.060	2.485	2.787
26	1.315	1.706	2.056	2.479	2.779
27	1.314	1.703	2.052	2.473	2.771

a) (-5.776, 25.515)

b) (11.199, 28.290)

c) (12.694, 26.785)

d) (16.327, 23.168)