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?
2) Suppose the original regression is given by y = β0 + β1x1 + β2x2 + β3x3 + u. You want to test for heteroscedasticity using F test. What auxiliary regression should you run? What is the null hypothesis you need to test?
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...
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. b....
.Suppose I estimate the equation y = β0 + β1x1 + e when the true equation is y = α0 + α1x1 + α2x2 + e. Show that βˆ 1 will suffer from omitted variable bias.
When estimating y = β0 + β1x1 + β2x2 + β3x3 + ε, you wish to test H0: β1 = β2 = 0 versus HA: At least one βi ≠ 0. The value of the test statistic is F(2,20) = 2.50 and its associated p-value is 0.1073. At the 5% significance level, the conclusion is to ________. Multiple Choice a. reject the null hypothesis; we can conclude that x1 and x2 are jointly significant b. not reject the null hypothesis;...
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...
1.7. Consider a multiple regression model: y Ao + β1x1 + β, x2 +11. Which of the following is the correct way to find the OLS estimate B using the "partialling out" technique? (a) Run y-%+71x1+1. and obtain r. Then run 3: α° + ait e, al will be equal to y-a0 + α|r + e. ai will be equal to β . run y-a, +ar+e.ử, will be equal to B run y-a, +ar+e.ử, will be equal to β b)...
Question 1 1. [1 point] Suppose the regression model is logarithmic: log(Y ) = β1 + β2 log(X) + u. The estimate of β2 is 0.035. What is the interpretation of this coefficient? 2. [1 point] Suppose the regression model is semi-logarithmic: log(Y ) = β1 + β2X + u. The estimate of β2 is 0.035. What is the interpretation of this coefficient? 3. [1point]Supposetheregressionmodelhasquadraticterm: Y =β1+β2X+β3X2+u. The estimate of β2 is 0.035. What is the interpretation of this coefficient?...
1) Given the model y = βο + β1X1 + β2X2 + β3X3 + ε if we plot y against X1 and get a parabola shaped curve then what does this suggest? Choose the correct answer. a) E(ε) does not equal zero b) an X12 term is needed c) an X22 term is needed d) constant variance violated
a,b,c,d
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume that the true model satisfies all five standard assumptions of a simple regression model discussed in class. (a) Does the regression model we are running satisfy the zero conditional mean assumption? (b) Find the expected value of A (given X values). (e) Does the regression model we are running satisfy homoscedasticity? d) Find the variance of pi (given X...