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21 Cards in this Set
- Front
- Back
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 |
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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 |
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The regression R^2 is a measure of |
the goodness of fit of your regression line |
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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 |
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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 |
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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. |
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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 |
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To decide whether or not the slope coefficient is small or large you should |
analyze the economic importance of a given increase in X |
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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 |
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A binary variable is often called a |
dummy variable |
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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] |
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The 95% confidence interval for the beta_0-hat is the interval |
(beta_0-hat - 1.96SE, beta_0-hat + 1.96SE) |
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The OLS residuals, u_i-hat, are sample counterparts of the population |
error |
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Binary variables |
can only take on two values |
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In the simple linear regression model , the regression slope |
indicates by how many units Y increases given a one unit increase in X |
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The t-statistic is calculated by dividing |
the estimator minus its hypothesized value by the standard error of the estimator |
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the slope estimator, beta_1, has a smaller standard error, other things equal, if |
there is more variation in the explanatory variable, X |
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The sample regression line estimated by OLS |
will always run through point (X-bar, Y-bar) |
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The confidence interval for the sample regression function slope |
can be used to conduct a test about a hypothesized population regression function slope |
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The regression R^2 is defined as follows |
(ESS / TSS) |
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This question was too long to type-- |
See question 6 for practice! |