1. Question 1: An economist is interested in characterizing the impact of povert

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Question

1. Question 1: An economist is interested in characterizing the impact of poverty level on educa- tion level. Poverty level is defined as the percent of the states population living in households with incomes below the federally defined poverty level. Some recent data are tabulated below. (Data source: Mind On Statistics, 3rd edition, Utts and Heckard) Education level (yrs) 8.5 12.1 7.8 19.411..2 Poverty level 31.5 18.935 14.4 16.7 (a) Write down the regression model explaining the impact of poverty on education. Explain (b) Calculate the OLS estimates of the intercept and slope. (Hint: 21.14 and A (c) Calculate R2 and adj. R2. Explain what these numbers mean. (Hint: R20.65 and (d) If the poverty rate in another state was 25%, what number for the predicted level of the meanings of the intercept and slope coefficients. -0.81.) R2-0.53.) education can you come up with?

Explanation / Answer

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a) The regression model will be

Educ = 0 + 1*Poverty + u where Educ is the education level and Poverty represents the poverty level.

The intercept coefficient tells us the level of education when poverty level is kept 0. The slope coefficient tells us that if poverty level goes up by 1 percent education level on average will go down by 1 yerars

Education (Yi)

Poverty level (Xi)

(Xi -Xm)

(Yi-Ym)

(Xi-Xm)(Yi-Ym)

(Xi-Xm)2

(Yi-Ym)2

8.5

31.5

8.2

-3.3

-27.06

67.24

10.89

12.1

18.9

-4.4

0.3

-1.32

19.36

0.09

7.8

11.7

-4

-46.8

136.89

19.4

14.4

-8.9

7.6

-67.64

79.21

57.76

11.2

16.7

-6.6

-0.6

3.96

43.56

0.36

Total

-2.3E-14

-6.2E-15

-138.86

346.26

85.1

1 = (Xi-Xm)(Yi-Ym)/(Xi-Xm)2

1_hat = (-138.86)/346.26

1_hat = -0.40

0_hat =Ym - (1_hat)*Xm

0_hat = 11.8 +0.4*23.3 = 11.8+0.4*23.3 =21.12

R2 = [Cov(Xi, Yi)]2/Var(Xi)*Var(Yi)

R2 = (-138.86)2/(346.26)*(85.1) = 0.65

Adjusted R2 =1-[(1-R2)(N-1)/(N-p-1)]

Adjusted R2= 1-[(0.35*4)/3] =0.53

The R2 tells us that 65% variation in education is explained by poverty levels.

Adjusted R2 is the r2 adjusted for the degrees of freedom.

Educ= 21.12-0.4*25 = 11.12 years