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21 Cards in this Set
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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_1hat^act
2. Compute the tstatistic
3. Compute the pvalue 

Consider the eqn:
Testscorehat = 698.9  2.28 = 698.9 2.28STR (10.4) (0.52)
R^2 = 0.051 SER = 18.6
tstatistic? 
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_1hat? 
beta_1 is the true population parameter, the slope of the population regression line, while beta_1hat is the OLS estimator of beta_1 

What is the difference between u and uhat? 
u represents the deviations of observations from the population regression line, while uhat is the difference between Y and Yhat 

What is the difference between the OLS predicted value Yhat and E(YX)? 
E(YX) is the expected value of Y given values of X, while Yhat 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:
Testscorehat = 698.9  2.28STR slope coefficient tstat = 4.38
What is the standard error of slope coefficient? 
0.52 

A binary variable is often called a 
dummy variable 

if
ahehat = 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_0hat is the interval 
(beta_0hat  1.96SE, beta_0hat + 1.96SE) 

The OLS residuals, u_ihat, 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 tstatistic 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 (Xbar, Ybar) 

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! 