The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 16 In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean? The probability that the null hypothesis is true is 0.5% The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5% The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5 It does not mean anything, because the significance level can only be set at 5%
The Simple Linear Regression model is
Y = b0 + b1*X1 + u
and the Multiple Linear Regression model with k variables is:
Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u
Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,
Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients.
QUESTION 16
In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean?
- The
probability that the null hypothesis is true is 0.5% - The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5%
- The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5
- It does not mean anything, because the significance level can only be set at 5%
QUESTION 17
In an MLR model with 550 observations and 5 explanatory variables and a constant, suppose you want to conduct a two-tailed t-test, with the null hypothesis being that a coefficient is equal to 1. Given that assumptions MLR1-MLR6 hold, if the estimated coefficient is equal to 1.5 and the standard error of this coefficient is 0.25, which of the following is correct?
- We can reject the null hypothesis at 10% level of significance but not at 5% level of significance
- We can reject the null hypothesis at 5% level of significance but not at 1% level of significance
- We can reject the null hypothesis at 1% level of significance
- You cannot reject the null hypothesis even at 10% level of significance
QUESTION 18
Suppose you want to conduct a two-tailed t-test and that your t-statistic (in absolute value) is equal to 10. Given that assumptions MLR1-MLR6 hold, and that you have 500 degrees of freedom, what is the p-value?
- Very close to one
- Very close to 10
- Very close to the true value of the slope coefficient
- Very close to zero
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