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Specify the 3 steps required to test the null hypothesis that the slope coefficient beta_1 equals zero.

1. Compute the standard error of the estimated slope coefficient beta_1-hat^act



2. Compute the t-statistic



3. Compute the p-value

Consider the eqn:



Testscore-hat = 698.9 - 2.28 = 698.9 -2.28STR


(10.4) (0.52)



R^2 = 0.051


SER = 18.6



t-statistic?

4.38

The regression R^2 is a measure of

the goodness of fit of your regression line

What is the difference between beta_1 and beta_1-hat?

beta_1 is the true population parameter, the slope of the population regression line, while beta_1-hat is the OLS estimator of beta_1

What is the difference between u and u-hat?

u represents the deviations of observations from the population regression line, while u-hat is the difference between Y and Y-hat

What is the difference between the OLS predicted value Y-hat and E(Y|X)?

E(Y|X) is the expected value of Y given values of X, while Y-hat is the OLS predicted value of Y for given values of X.

In the simple linear regression model Y_i = beta_0 + beta_1X_i + u_i, what does beta_0 + beta_1X_i represent?

the population regression function

To decide whether or not the slope coefficient is small or large you should

analyze the economic importance of a given increase in X

Consider the following regression line:



Testscore-hat = 698.9 - 2.28STR


slope coefficient t-stat = 4.38



What is the standard error of slope coefficient?

0.52

A binary variable is often called a

dummy variable

if



ahe-hat = 3.32 - 0.45Age, R^2 = 0.02, SER=8.66


(1.00) (0.04)



the 95% confidence interval for the effect of changing age by 5 years is approximately

[1.96,2.54]

The 95% confidence interval for the beta_0-hat is the interval

(beta_0-hat - 1.96SE, beta_0-hat + 1.96SE)

The OLS residuals, u_i-hat, are sample counterparts of the population

error

Binary variables

can only take on two values

In the simple linear regression model , the regression slope

indicates by how many units Y increases given a one unit increase in X

The t-statistic is calculated by dividing

the estimator minus its hypothesized value by the standard error of the estimator

the slope estimator, beta_1, has a smaller standard error, other things equal, if

there is more variation in the explanatory variable, X

The sample regression line estimated by OLS

will always run through point (X-bar, Y-bar)

The confidence interval for the sample regression function slope

can be used to conduct a test about a hypothesized population regression function slope

The regression R^2 is defined as follows

(ESS / TSS)

This question was too long to type--

See question 6 for practice!