1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct?
| a. |
When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. |
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| b. |
When drawing ceteris paribus conclusions about how x1 affects y, with model (2), because x2 is explicitly in the model equation, we are able to measure the effect of x1 on y, holding x2 fixed—assuming all other factors contained in u, are uncorrelated with x1 and x2. |
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| c. |
With a simple regression model like (1) or a multiple regression model like (2), if any other factor, not explicitly in the model equation and, thus contained in u, is correlated with any independent variable xj, then the OLS estimator of the slope parameter βj associated with that variable is biased. |
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| d. |
All of the above. |
2. Consider the following model: y = β0 + β1x1 + β2x12+ u (1). Which of the following statements is correct?
| a. |
Model (1) is a quadratic simple regression model. |
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| b. |
Model (1) is linear simple regression model. |
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| c. |
Model (1) is a quadratic multiple regression model. |
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| d. |
Model (1) is linear multiple regression model. |
3. Consider the following simple regression model: y = β0 + β1x12+ u (1). Which of the following statements is correct?
| a. |
The effect of x1 on y, is measured by β1. |
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| b. |
The effect of x1 on y, is measured by 2β1x1. |
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| c. |
The effect of x1 on y, is measured by β0 + 2β1x1. |
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| d. |
All of the above. |
1. c). With a simple regression model like (1) or a multiple regression model like (2), if any other factor, not explicitly in the model equation and, thus contained in u, is correlated with any independent variable xj, then the OLS estimator of the slope parameter βj associated with that variable is biased.
it's the assumption of linear simple regression and multiple regression analysis
2). d). model y = β0 + β1x1 + β2x12+ u (1) is linear multiple regression model
3). b). The effect of x1 on y, is measured by 2β1x1. => β0 shows the effect on y when x1 = 0 and β1x12 show effect of x1 on y
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and...
Suppose the true model is given by y = β0 + β1x1 + β2 x2 + u , if we estimate the following models: (I) y = β0 + β1x1 + β2 x2 + β3x3 + u (II) y = β0 + β1x1 + u what are the consequences?
Exhibit a. y = β0 + β1x1 + β2x2 + ε b. E(y) = β0 + β1x1 c. = b0 + b1 x1 + b2 x2 d. E(y) = β0 + β1x1 + β2x2 3. Refer to Exhibit. Which equation describes the multiple regression equation? a. equation a b. equation b c. equation c d. equation d
1. Functional form misspecification and RESET Consider the following model that satisfies assumption MLR.4: y=β0+β1x1+. . .+βkxk+u Which of the following describes the regression specification error test (RESET)? PICK all that apply. RESET picks up all kinds of neglected nonlinearities when more quadratic terms are added to the original model. RESET works better when there are many explanatory variables in the original model, as it increases its degrees of freedom. To implement RESET, the researcher must add at least seven...
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming a conditional variance function Varux=σ2h(x). Which of the following statements is correct? A) The function h(x) does not need to be estimated as part of the procedure B) If the assumption about the conditional variance of the error term is incorrect, then FWLS is still consistent. C) FWLS is the best linear unbiased estimator when there is heteroscedasticity. D) None of the above answers...
Consider the following formulations of the 1 variable regression model: Y = β0 + β1x + u and Y = α0 + α1(x − ¯x) + a a) would the estimates of β0 and α0 the same? Explicitly shows this by deriving the estimates. b) What about β1 and α1 ? c) In the regression Y = β0 +β1x+u suppose we multiply each X value by a constant, say, 2. Will it change the residuals and fitted values of Y?...
1. What is Frisch-Waugh Theorem? Express it in algebraic terms in a multiple linear regression model y = β0 + β1x1 + β2 x2 + u
1. When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with ____________________. df1 = k and df2 = n – k – 1 df1 = k – 1 and df2 = n – k – 1 df1 = r and df2 = n – k df1 = r and df2 = n – k – 1 2. (Round...
31. Suppose you fit a multiple linear regression model y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε to n = 30 data points and obtain SSE = 282 and R^2 = 0.8266 a.) Find an estimate of s^2 for the multiple regression model (a) s^2 ≈ 30.9856 (b) s^2 ≈ 28.6021 (c) s^2 ≈ 1.3111 (d) s^2 ≈ 29.7938 (d) b.) Based on the data information given in a.), you use F-test to test H0...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α...