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Unformatted text preview: Department of Economics Spring 2006 University of California, Berkeley Prof Woroch Problem Set 2 Suggested Answers 1 You are given the following results from the regression of expenditures of imported goods on per capita income: Y t =- 261 . 09 + 0 . 2453 * X t Std Error = (31 . 320) (0 . 015) R 2 = 0 . 9388 t = (8 . 34) (16 . 616) n = 20 (1) where Y t is the consumption of imported goods for the U.S., X t is per capita income, and t [1968-1987]. a. Fill in the blanks. b. Give your economic and econometric interpretations of the two estimated coefficients from the regression: when the income per capita increases by $100, the consumption of imported goods per capita increases on average by $25. If the per capita income were equal to 0, the consumption of imported goods would be on average -261.09 dollars (it doesnt make much sense though, because the income per capita will never be equal to 0). c. Is the slope coefficient different from zero? At what significance level? What is the associated p-value? The slope coefficient 1 has a t-value of 16.616. Here we have n = 20 observations, so we need to compute the t n- 1 , 1- / 2 threshold. We see that for 19 degrees of freedom (20-1=19), the t-value for a 1% significance level is 2.54, so we reject the null hypothesis (we accept that the coefficient is significant) at least at the 1% S.L. The p-value associated is close to 0. d. Given the R 2 value, do you believe that higher expenditures on imported goods leads to higher personal income? Explain your reasoning. R 2 is close to 1, meaning that the regres- sion line almost goes through the points. Knowing that the per capita income leads to highersion line almost goes through the points....
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