Consider the linear function y, = Bo + Bix,+ u. Suppose that the following results were obtained from a sample with 12 observations: 2 3. 4. Sample covariance of y and x = 10. Suppose that the CLM Assumptions hold here and answer the following questions. 1. Calculate the OLS estimates of Bo and B₁, and the R². [Hint: R2 is equaled to the square of "coefficient of correlation", r.] 5. . 6. XFIXI BAD ALL Sample average of y = 20 Sample average of x = 20 Sample variance of y = 20 Sample variance of x = 10 Estimate the variance of error term, o, and Var (₁). [Hint: See eq. (2.61).] Test the null hypothesis that x has no effect on y against the alternative that x has effect on y, at the 5% and 1% significance levels. Suppose that we add the term z to the original model and that x and z are negatively correlated. What is the likely bias in estimates of Bi obtained from the simple regression of y on x if ß₂ <0? Based on question 4, when R² = 0.75 from regressing y on x and z, what is the t-statistic for the coefficient on z? Can we say that "z is statistically significant?" Based on question 4, suppose that x is highly correlated with z in the sample, and z has large partial effects on y. Will the bias in question 4 tend to be large or small? Explain.
Consider the linear function y, = Bo + Bix,+ u. Suppose that the following results were obtained from a sample with 12 observations: 2 3. 4. Sample covariance of y and x = 10. Suppose that the CLM Assumptions hold here and answer the following questions. 1. Calculate the OLS estimates of Bo and B₁, and the R². [Hint: R2 is equaled to the square of "coefficient of correlation", r.] 5. . 6. XFIXI BAD ALL Sample average of y = 20 Sample average of x = 20 Sample variance of y = 20 Sample variance of x = 10 Estimate the variance of error term, o, and Var (₁). [Hint: See eq. (2.61).] Test the null hypothesis that x has no effect on y against the alternative that x has effect on y, at the 5% and 1% significance levels. Suppose that we add the term z to the original model and that x and z are negatively correlated. What is the likely bias in estimates of Bi obtained from the simple regression of y on x if ß₂ <0? Based on question 4, when R² = 0.75 from regressing y on x and z, what is the t-statistic for the coefficient on z? Can we say that "z is statistically significant?" Based on question 4, suppose that x is highly correlated with z in the sample, and z has large partial effects on y. Will the bias in question 4 tend to be large or small? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![Consider the linear function y; = Bo + Bix+u. Suppose that the following results were obtained
from a sample with 12 observations:
2
3.
4.
Sample covariance of y and x = 10.
Suppose that the CLM Assumptions hold here and answer the following questions.
1.
Calculate the OLS estimates of Bo and B₁, and the R². [Hint: R2 is equaled to the square of
"coefficient of correlation", r.]
Estimate the variance of error term, o, and Var (₁). [Hint: See eq. (2.61).]
Test the null hypothesis that x has no effect on y against the alternative that x has effect on y, at
the 5% and 1% significance levels.
5.
.
6.
XFIXI B Att
Sample average of y=20
Sample average of x = 20
Sample variance of y = 20
Sample variance of x = 10
Suppose that we add the term z to the original model and that x and z are negatively
correlated. What is the likely bias in estimates of Bi obtained from the simple regression of y on
x if ß₂ <0?
Based on question 4, when R² = 0.75 from regressing y on x and z, what is the t-statistic for the
coefficient on z? Can we say that "z is statistically significant?"
7
Based on question 4, suppose that x is highly correlated with z in the sample, and z has large
partial effects on y. Will the bias in question 4 tend to be large or small? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05ed4213-5832-4388-9cf2-f1d506899ead%2F6e158409-59fc-446a-afc6-ac8705e3cd4c%2F1htsnvd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the linear function y; = Bo + Bix+u. Suppose that the following results were obtained
from a sample with 12 observations:
2
3.
4.
Sample covariance of y and x = 10.
Suppose that the CLM Assumptions hold here and answer the following questions.
1.
Calculate the OLS estimates of Bo and B₁, and the R². [Hint: R2 is equaled to the square of
"coefficient of correlation", r.]
Estimate the variance of error term, o, and Var (₁). [Hint: See eq. (2.61).]
Test the null hypothesis that x has no effect on y against the alternative that x has effect on y, at
the 5% and 1% significance levels.
5.
.
6.
XFIXI B Att
Sample average of y=20
Sample average of x = 20
Sample variance of y = 20
Sample variance of x = 10
Suppose that we add the term z to the original model and that x and z are negatively
correlated. What is the likely bias in estimates of Bi obtained from the simple regression of y on
x if ß₂ <0?
Based on question 4, when R² = 0.75 from regressing y on x and z, what is the t-statistic for the
coefficient on z? Can we say that "z is statistically significant?"
7
Based on question 4, suppose that x is highly correlated with z in the sample, and z has large
partial effects on y. Will the bias in question 4 tend to be large or small? Explain.
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