Consider the regression model. Y = beta_1 + beta_2 X_2 + beta_3 X_3 + epsilon No
ID: 3300704 • Letter: C
Question
Consider the regression model. Y = beta_1 + beta_2 X_2 + beta_3 X_3 + epsilon Now assume that there are 100 observations and that the available data are in the form of deviation from sample means, so that x_2 = X_2 - X_2, x_3 = X_3 - X_3, and y = Y - Y. Therefore, y = beta_2 x_2 + beta_3 x_3 + epsilon You already know the following results: x'x = [x'_2 x_2 x'_3 x_2 x'_2 x_3 x'_3 x_3] = [10 -5 -5 20], x'y = [15 80], i' Y = 10,000, i' X_2 = 800, and i' X_3 = 1000 And, finally, you also know the inverse of a 2 times 2 matrix: [a c b d]^-1 = 1/ad - bc [d -c -b a] (a) What are the OLS estimates b for beta_2 and beta_3? (b) Since the data are in deviations from the mean, find the intercept (or constant coefficient), beta_1.Explanation / Answer
a) b^ = (inv( x'x ))*x'y
(inv( x'x )) =
0.1143 0.0286
0.0286 0.0571
b^ =
4
5
b2 = 4 , b3 = 5
b) b1 = ybar - b2*x2bar - b3 *x3bar
ybar = 100 , x2bar =8 ,x3bar = 10
b1 = 100 - 4*8 - 5*10
= 18
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