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 25 In the MLR model, with 150 observations and 5 explanatory variables, suppose you want to test the null hypothesis, H0: b3=0, b4=0 We also know that the RSS of the unrestricted model is 563, while the RSS of a model that excludes the variables associated with the 2 coefficients under the null hypothesis is 577. Given this information what is the F-statistic for this hypothesis? It is around -1.79 It is around 1.75 It is around -1.75 It is around 1.79
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 25
In the MLR model, with 150 observations and 5 explanatory variables, suppose you want to test the null hypothesis,
H0: b3=0, b4=0
We also know that the RSS of the unrestricted model is 563, while the RSS of a model that excludes the variables associated with the 2 coefficients under the null hypothesis is 577. Given this information what is the F-statistic for this hypothesis?
- It is around -1.79
- It is around 1.75
- It is around -1.75
- It is around 1.79
QUESTION 26
In the MLR model, with 1000 observations and 10 explanatory variables, suppose you want to test the null hypothesis:
H0: b5=0, b6=0, b7=0, b8=0, b9=0
We know that the R-squared of the unrestricted model is 0.40, while the R-squared of a model that excludes the variable associated with the coefficients under the null hypothesis is 0.39. Given this information, which of the following statements is correct?
- We can reject the null hypothesis at 1% 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 10% level of significance, but not at 5% level of significance
- We cannot reject the null hypothesis even at 10% level of significance
QUESTION 27
Suppose you have an MLR model with 6 variables, and that the t-statistic associated with the 6th variable of this model is -0.5. Suppose this 6th variable is now removed, and the model is re-estimated by OLS.
What will happen to the Adjusted R-squared, as we move from the model with 6 variables to the model with 5 variables?
- It is not possible to say with the provided information
- It will decrease
- It will remain the same
- It will increase
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