Question

You have the results of a simple linear regression based on state-level data and the (a) The estimated error variance .04672. What is the sum of the squared least (b) The estimated variance of ba is 0.00098. What is the standard error of b2? What 2.7 District of Columbia, a total of N- 51 observations. squares residuals? is the value of Σ(x- 2? (c) Suppose the dependent variable y the state's mean income (in thousands of dollars) of males who are 18 years of age or older and x the percentage of males 18 years or older who are high school graduates. If b-0.18, interpret this result. (d) Suppose (e) Given the results in (b) and (d), what is ΣΧΡ 69.139 and y 15.187, what is the estimate of the intercept parameter? (f) For the state of Arkansas the value ofy 12.274 and the value of x58.3. Compute the least squares residual for Arkansas. (Hint: Use the information in parts (c) and (d).).

All parts please.

Answer 1

N = 51, (s) sigma^^2 = 2.04672, then simple Reg^n, 2 variable sigma^^2 = sigma e i^2/n - 2 so sigma ei^2 rightarrow sum of Residual squares = (51 - 2) times sigma^^2 = 49 times 2.04672 = 100.28928 b) (b_2) = .00098 se = squareroot var (b_2) sigma x^2_i = sigma (x_i - x^-)^2, as v(b_2) = sigma^^2/sigma xi^2, so sigma xi^2 = 2.04672/.00098 = 2088.4898 c) Now yi rightarrow Mean income of 18 years old Moles. b_2 = .18, y_i = beta_0 + beta_2 x_i + u_i 80 b_2 imply that of % of 18 years or older Male uparrow by 190, then on an average, Mean income of this of uparrow by .1890 beta_2 = d y_i/dx_i rightarrow {so d y_i = beta_2 d x_i} d) Now x^- = 69.139, y^- = 15.187, then beta^^_0 = y^- - beta^^_2 x^- intercept = (15.187) - beta^^_2 times (69.139) parent = (15.187)