Question

Just as you are about to estimate a regression (due tomorrow), massive sunspots cause magnetic interference that ruins all electrically powered machines (e.g., computers). Instead of giving up and flunking, you decide to calculate estimates from your data (on per capita income in thousands of U.S. dollars as a function of the percent of the labor force in agriculture in 10 developed countries) using methods like those used in Section 2.1 (Yi = B0 + B1Xi + Ei) without using a computer. Your data are:Country A B C D E F G H I JPer Capita Income 6 8 8 7 7 12 9 8 9 10% in Agriculture 9 10 8 7 10 4 5 5 6 7a.) Calculate Beta-hat zero and Beta-hat one.b.) Calculate R2(r-squared) and R`2 (adjusted r-squared).c.) If the percent of the labor force in agriculture in another developed country was 8 percent, what level of per capita income (in thousands of U.S. dollars) would you guess that country had?

Answer 1

A) Beta-hat one = -0.547

Beta-hat zero = 12.2837

b) attached

C) y = $7.904

Explanation:

hello attached below is the detailed solution and the table

A) Calculate Beta-hat Zero and Beta-hat one

Beta-hat one :

∑ ( xi - x ) (yi - y ) / ∑ (xi - x )^2

= -22.4 / 40.9 = -0.547

Beta-hat zero :

Y - Beta-hat one * X

= 8.4 - (-0.547 )(7.1 ) = 12.2837

B) Calculate R^2 and R^2

attached below

C) using Regression equalia to determine the level of per capita income

y = 12.28 - 0.547 * x

where x = 8

hence Y = $7.904