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 22 Suppose your estimated MLR model with two explanatory variables, X1 and log(X2), is: log(Y)_hat= 10 +0.5*X1 + 0.25*log(X2) Which of the following statements about the interpretation of the coefficient of log(X2) is correct? If X2 increases by 1%, Y is predicted to increase by approximately 25 units, holding X1 constant If X2 increases by 1%, Y is predicted to increase by approximately 0.25%, holding X1 constant If X2 increases by 1 unit, Y is predicted to increase by approximately 25%, holding X1 constant If X2 increases by 1 unit, Y is predicted to increase by approximately 0.25 units, holding X1 constant QUESTION 23 Suppose your estimated MLR model is: Y_hat= 10 + 3*X + 12*D – 1.5*(X*D) where X is a continuous variable, D is a dummy variable (i.e. taking only values 0 and 1), and X*D is the interaction term between the two variables. What is the predicted change in Y, if X goes up by 1 unit, given that D=1? Y is predicted to increase by 12 units Y is predicted to decrease by 1.5 units Y is predicted to increase by 3 units Y is predicted to increase by 1.5 units QUESTION 24 Suppose your estimated MLR model is: Y_hat= 10 + 3*X + 12*D – 1.5*(X*D) where X is a continuous variable, D is a dummy variable (i.e. taking only values 0 and 1), and X*D is the interaction term between the two variables. What is the interpretation of the estimated coefficient associated with variable X? It is the estimated effect of X on Y for D=1 It is the estimated effect of X on Y holding D constant It is the estimated effect of Y on X for D=1 It is the estimated effect of X on Y for D=0
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 22
Suppose your estimated MLR model with two explanatory variables, X1 and log(X2), is:
log(Y)_hat= 10 +0.5*X1 + 0.25*log(X2)
Which of the following statements about the interpretation of the coefficient of log(X2) is correct?
- If X2 increases by 1%, Y is predicted to increase by approximately 25 units, holding X1 constant
- If X2 increases by 1%, Y is predicted to increase by approximately 0.25%, holding X1 constant
- If X2 increases by 1 unit, Y is predicted to increase by approximately 25%, holding X1 constant
- If X2 increases by 1 unit, Y is predicted to increase by approximately 0.25 units, holding X1 constant
QUESTION 23
Suppose your estimated MLR model is:
Y_hat= 10 + 3*X + 12*D – 1.5*(X*D)
where X is a continuous variable, D is a dummy variable (i.e. taking only values 0 and 1), and X*D is the interaction term between the two variables. What is the predicted change in Y, if X goes up by 1 unit, given that D=1?
- Y is predicted to increase by 12 units
- Y is predicted to decrease by 1.5 units
- Y is predicted to increase by 3 units
- Y is predicted to increase by 1.5 units
QUESTION 24
Suppose your estimated MLR model is:
Y_hat= 10 + 3*X + 12*D – 1.5*(X*D)
where X is a continuous variable, D is a dummy variable (i.e. taking only values 0 and 1), and X*D is the interaction term between the two variables. What is the interpretation of the estimated coefficient associated with variable X?
- It is the estimated effect of X on Y for D=1
- It is the estimated effect of X on Y holding D constant
- It is the estimated effect of Y on X for D=1
- It is the estimated effect of X on Y for D=0
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