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Suppose we have 51 observations on income per capita (y) and the percentage of population with a bachelor's or higher degree (x). Using this data, the following regression model has been estimated: y = (a) + 1.029x se (2.672) (c) t (4.31) (10.75), where se stands for the standard errors of the estimated coefficients b1 and b2; t stands for the t-ratios of the two estimated regression coefficients (b, and b2) when testing the hypothesis H,:b1,2 = 0, Ha: b12 + 0. (H5:3.7) a. Calculate the estimated intercept, b1. Interpret (explain the meaning) of the two regression coefficients, bị and b2. (Please remember that the t-ratio is equal to the estimated value of a parameter over its standard error when testing the null hypothesis that the parameter is equal to zero.)

Suppose we have 51 observations on income per capita (y) and the percentage of population with a bachelor's or higher degree (x). Using this data, the following regression model has been estimated: y = (a) + 1.029x se (2.672) (c) t (4.31) (10.75), where se stands for the standard errors of the estimated coefficients b1 and b2; t stands for the t-ratios of the two estimated regression coefficients (b, and b2) when testing the hypothesis H,:b1,2 = 0, Ha: b12 + 0. (H5:3.7) a. Calculate the estimated intercept, b1. Interpret (explain the meaning) of the two regression coefficients, bị and b2. (Please remember that the t-ratio is equal to the estimated value of a parameter over its standard error when testing the null hypothesis that the parameter is equal to zero.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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国 14. Suppose we have 51 observations on income per capita (y) and the percentage of population with a bachelor's or higher degree (x). Using this data, the following regression model has been estimated: y = (a) + 1.029x se (2.672) (c) t (4.31) (10.75), where se stands for the standard errors of the estimated coefficients b, and b2; t stands for the t-ratios of the two estimated regression coefficients (b, and b2) when testing the hypothesis Ho:b12 0, Ha: b1,2 + 0. (H5:3.7) a. Calculate the estimated intercept, b1. Interpret (explain the meaning) of the two regression coefficients, b, and b2. (Please remember that the t-ratio is equal to the estimated value of a parameter over its standard error when testing the null hypothesis that the parameter is equal to zero.) b. Sketch the estimated relationship. it increasing, or decreasing? Is it a positive, or negative relationship? Is it increasing or decreasing at a constant rate, or is it increasing or decreasing at an increasing or decreasing rate? С. Calculate the standard error of the slope coefficient b2 of the regression model. Show your work. d. What is the value of the t-statistic for the null hypothesis that the intercept is equal to 10? The p-value of the two-tail test that the intercept parameter equals 10 from part (d) is 0.572. Show the p-value in a sketch. On the sketch, show the rejection region if a = 0.05. Construct a 99% interval estimate of the slope coefficient, b2. Interpret the interval estimate. g. Test the null hypothesis that the slope coefficient is equal to 1 against the alternative that it is е. f. not 1 at the 5% level of significance. State the economic result of the test in the context of this problem.
Transcribed Image Text:国 14. Suppose we have 51 observations on income per capita (y) and the percentage of population with a bachelor's or higher degree (x). Using this data, the following regression model has been estimated: y = (a) + 1.029x se (2.672) (c) t (4.31) (10.75), where se stands for the standard errors of the estimated coefficients b, and b2; t stands for the t-ratios of the two estimated regression coefficients (b, and b2) when testing the hypothesis Ho:b12 0, Ha: b1,2 + 0. (H5:3.7) a. Calculate the estimated intercept, b1. Interpret (explain the meaning) of the two regression coefficients, b, and b2. (Please remember that the t-ratio is equal to the estimated value of a parameter over its standard error when testing the null hypothesis that the parameter is equal to zero.) b. Sketch the estimated relationship. it increasing, or decreasing? Is it a positive, or negative relationship? Is it increasing or decreasing at a constant rate, or is it increasing or decreasing at an increasing or decreasing rate? С. Calculate the standard error of the slope coefficient b2 of the regression model. Show your work. d. What is the value of the t-statistic for the null hypothesis that the intercept is equal to 10? The p-value of the two-tail test that the intercept parameter equals 10 from part (d) is 0.572. Show the p-value in a sketch. On the sketch, show the rejection region if a = 0.05. Construct a 99% interval estimate of the slope coefficient, b2. Interpret the interval estimate. g. Test the null hypothesis that the slope coefficient is equal to 1 against the alternative that it is е. f. not 1 at the 5% level of significance. State the economic result of the test in the context of this problem.
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