1. Consider the following data on education (years, X) and wages ($/hour, Y) a. b. ED 16 13 18 10 14 8 WAGE 13 9 11 12 3 8 Plot by-hand the above data in scatter-plot form, and comment on a likely relationship. Be sure the plot is well done and labeled appropriately. Consider the following model of wages Y, B₁ + B₂X, +u, Using OLS, estimate the slope and intercept parameters by-hand, and plot the fitted regression line on the above scatter-plot. Interpret the meaning of the true and estimated intercept and slope./nShow all work. If numerical answers are provided without proof of work-by-hand, no credit will be given. Derive the Error Sum of Squares [ESS], the standard error of the regression, and the standard errors of the estimated slope and intercept. Derive 95% CI's for both estimators, and comment on their tightness. Perform standard tests of the hypotheses that the true slope is zero and the true parameters is zero. That is, test both C. d. e. H₁: B₁ = 0 H, B, 0 In order to perform the tests, do the following: i. ii. H₁: B₂=0 H₁: B₂ 0 iii. Present the t-statistic formula, and state its distribution under the null. Present the critical values for a test at the 5% level, and compute the p-values. Comment on the results of the tests and how they relate to the confidence intervals.

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1. Consider the following data on education (years, X) and wages ($/hour, Y) a. b. ED 16 13 18 10 14 8 WAGE 13 9 11 12 3 8 Plot by-hand the above data in scatter-plot form, and comment on a likely relationship. Be sure the plot is well done and labeled appropriately. Consider the following model of wages Y, B₁ + B₂X, +