Econometrics question 5. Consider the regression model Y; = B,X1; + B2X2; + B3 (X1i * X2i) + Uj. Show that(a) AY/AX1 = B1+ B3X2 (effect of a change in X1 holding X2 constant).(b) AY/AX2 = B1 + B3X1 (effect of a change in X2 holding X1 constant).(c) If X1 changes AX1 and X2 changes AX2, thenAY = (81 + B3X2) AX1 + (B2 + B3X1) AX2+ B3AX1AX2.

Given:Yi=β1X1i+β2X2i+β3(X1i* X2i) + Ui

Consider the regression model Y; = B1X1¡ + B2X2; + B3 (X1i * X2;) + Uj. Show that (a) AY/AX1 = B1 + B3X2 (effect of a change in X1 holding X2 constant). (b) AY/AX2 = ß1 + B3X1 (effect of a change in X2 holding X1 constant). (c) If X1 changes AX1 and X2 changes AX2, then AY = (B1 + B3X2) AX1 + (B2 + B3X1)AX2+ B3AX1AX2.

Consider the regression model Y; = B1X1¡ + B2X2; + B3 (X1i * X2;) + Uj. Show that (a) AY/AX1 = B1 + B3X2 (effect of a change in X1 holding X2 constant). (b) AY/AX2 = ß1 + B3X1 (effect of a change in X2 holding X1 constant). (c) If X1 changes AX1 and X2 changes AX2, then AY = (B1 + B3X2) AX1 + (B2 + B3X1)AX2+ B3AX1AX2.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4: Estimating Demand

Section: Chapter Questions

Problem 1.4CE

See similar textbooks

Similar questions

5 We are given a sample of n observations which satisfies the following regression model: yi = β0 + β1xi1 + β2xi2 + ui , for all i = 1, . . . , n. This model fulfills the Least-Squares assumptions plus homoskedasticity. (a) Explain how you would obtain the OLS estimator of the coefficients {β0, β1, β2} in this model. (You do not need to show a full proof. Writing down the relevant conditions and explain)
Hello, please help me to solve the question (c) and (d) below.Consider this regression model (1) : Yt = β0 + β1 Ut + β2 Vt + β3 Wt + β4 Xt + εt ; where t= 1, ..., 75.We use OLS to estimate the parameters, producing the following model:Ŷt = 1.115 + 0.790 Ut − 0.327 Vt + 0.763 Wt + 0.456 Xt (0.405) (0.178) (0.088) (0.274) (0.017) Given that:R2 = 0.941; Durbin Watson stat DW = 1.907; RSS = 0.0757.(To answer the question, use the 5% level of significance, state clearly H0 and H1 that are tested, the test statistics that are used, and interpret the decisions.) (a) Describe the concepts of unbiasedness and efficiency. State the conditions required of regression (1) in order that the OLS estimators of the model parameters possess these properties. (b) Perform the following tests on the parameters of regression (1): (i) test whether the parameters β1, β2, β3 and β4 are individually statistically significant; (ii) test the overall significance of the regression model;…
4- The manager of Collins Import Autos believes the number of cars sold in a day(Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working that day (S ). After collecting data for two months (53 days), the manager estimates the following log-linear model: Q = aHbSc ----- a. Explain how to transform this log-linear model into a linear form that can be estimated using multiple regression analysis. b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance level.
Suppose you have run four regression models: A, B, C, and D. You are going to make a decision on which one to use just based on the adjusted r² value. Here are the adjusted r² values for each model: A: 0.71 B: 0.57 C: 0.65 D: 0.76 Which regression model would you choose based on the adjusted r²? OD since it has the highest adjusted r² value B since it has the lowest adjusted r² OC since it has an adjusted r² between the adjusted r² of regressions B and D. Either B or C since they have the lowest adjusted r²
2. Which of the following types of regressions will always have a binary outcome variable? (A) Probit (B) Difference-in-differences (C) Regression discontinuity (D) (A) and (B) will both have binary outcome variables
A multiple regression model, K = a + bX + cY + dZ, is estimated regression software, which produces the following output: a. Are the estimates of a, b, c, and d statistically significant at the 1 percent significance level? b. How much of the total variation is explained by this regression equation? c. Is the overall regression equation statistically significant at the 1 percent level of significance? d. If X equals 50, Y equals 200, and Z equals 45, what value do you predict K will take?
In a simple linear regression equation, if X increases by 3: Select one: a. Y increases by B1 b. Y increases by B1/3 c. Y increases by 3 * (Bo + B1) d. none of the above
Consider the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied whena) Zi is independent of (Yi, Xi, Wi)?b) Zi=Wi?c) Wi is1 for all i?d) Zi=Xi?
Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted value of Y in each case? a. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 b. x1 = 23, x2 = 18, x3 = 10, and x4 = 11 c. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 d. x1 = -10, x2 = 13, x3 = -8, and x4 = -16
Given the regression equation Y = 100 + 10X a. What is the change in Y when X changes by +3? b. What is the change in Y when X changes by -4? c. What is the predicted value of Y when X = 12? d. What is the predicted value of Y when X = 23? e. Does this equation prove that a change in X causes a change in Y?
1) State in algebraic notation and explain the assumption about the classical linear regression models disturbances that are referred to by the term ‘homoscedasticity’.
q9- Which property of linear regression is related with the size effects of individual units in a cross-section data? Select one: a. Heteroskedasticity b. Endogeneity c. Autocorrelation d. Non-normality Clear my choice