3. An economist used the least squares procedure to fit a regression model of the formy₁ = B₁ + B₁x₁₁+ B₂x₂, +₁, where y is quantity demanded of a good (in million units),x₁ is price of the good (in cedis), x₂ is household income (in thousand cedis), and& ~ N(0,0²). Tabulated below are sums obtained 8 sets of observationsΣv=4832y =30567Σ.x,y = 3068Ex=53E x =365Σx₂y=3795Calculations have produced the following matrix(x'x) ¹ =[50.68462 -4.030770.33846Ex=60E x =472Σxx, = 382-3.18077]0.238460.21346a. Form the matrices: XX and X'Y.b. Use (X'X)¹ and X'Y to compute the OLS estimates for ß₁, i = 0,1,2.c. Write the fitted regression model and interpret the partial regression coefficients.d. Find the variance-covariance matrix, &² (X'X)¹¹.e. Use a = 0.05 to test the null hypothesis that B₁ <0. Discuss the findings.f. Use a = 0.05 to test the null hypothesis that B₂ = 0. Discuss the findings.g. Calculate and interpret R².h. Use a = 0.01 to test for significance of the fitted model. 2. An economist used the least squares procedure to fit a regression model of the formy₁ =B₁ + B₁x₁₁+ B₂x₂, +s, where y is the dependent variable, x₁, x₂ are independentvariables, and s, ~ N (0,0). Tabulated below are sums obtained from a randomsample of 25 observations in order to explain the dependent variable:Ev=5596Er =Σ.Χ.μ – 7375.44Calculations have produced the following matrix=18310.629Σχ = 219Σε=:(xx)' == 3055Σκv=337072Σχ. = 10232Ex=6725688Σxx, = 133899[0.11321518 -0.00444859 -0.000083670.00274378 -0.000047860.00000123Page 1 of 2a. Form the matrices: X'X and XY.b. Use (XX) and XY to compute the OLS estimates for p,, i=0,1,2.c. Write the fitted regression model and interpret the partial regression coefficients.d. Find the variance-covariance matrix, & (XX).e. Use a 0,05 to test the null hypothesis that B3, =0. Discuss the findings.f. Use = 0.05 to test the null hypothesis that , >0. Discuss the findings.g. Calculate and interpret R¹.h. Use a 0.01 to test for significance of the fitted model.

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Answered: 2. An economist used the least squares…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
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Find the least square regression line.
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