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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_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 = 0.051SER = 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 - 2.28STRslope 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!