The OLS residuals:

The error term is assumed to be a random variable with an expected value of zero, and this assumption implies that the variance of Y about the regression line is the same for all values of X.

https://courses.rsu.edu/bbcswebdav/pid-72660852-dt-asiobject-rid-48811505_1/xid-48811505_1?Kq3cZcYS15=292a4c725b7b48b0b5641545d1caa3e8&VxJw3wfC56=1761061862&3cCnGYSz89=kruJ7aUdQ133YXhuxTIwqQhPOzk8NSnW0C1bTbLw3EQ%3D

You have collected data for the 52 countries and estimated the following relationship between the change in the unemployment rate from the previous year ( ∆ u r ^ ) and the growth rate of the respective country real GDP (gy). The results are as follows: unemployment reg.png Assuming that the estimator has a normal distribution, the 95% confidence interval for the slope is approximately the interval:

hypothesis test(1).png  

Wage Reg.png  The wage of male workers, on average, is $18.3.

You are interested in the effect of number of homeruns (HomeRun) on the number of wins (Wins) in 2005 Major League Baseball (MLB) season. Using 2005 MLB data (aggregated at the team level), you run a simple linear regression and get the following results from Stata. MLB2005 ShortAnswerQuestion(1).png Using the Stata output above and α =0.05, answer the following questions.  (a) Develop the null and the alternative hypothesis of the slope coefficient significance test.  (b) Compute the test statistic.  (c) Findf the critical value. (d) Based on your answers above, conclude whether you reject or do not reject the null hypothesis.  (e) Compute the R2.  (f) Construct 95% confidence interval for the slopep coefficient. 

Consider the estimated equation: TestScore Reg(2).png The t-statistic for the slope is approximately:

In simple linear regression, the coefficient of covariance and the OLS estimate of population slope:

In the simple linear regression model (Y_i=β_0+β_1 X_i+u_i), the slope represents the