ads/QM 215%20Homework%20Assignment%2012.pdf QM215 Homework Assignment 12 1. A so
ID: 2907959 • Letter: A
Question
ads/QM 215%20Homework%20Assignment%2012.pdf QM215 Homework Assignment 12 1. A sociologist examines the relationship between the poverty rate and several socioeconomic factors. For the 50 states and the District of Columbia (n = 51), he collects data on the poverty rate (Y, in %), the percent of the population with at least a high school education (X?), median income (X2, in $1000s), and the mortality rate per 1,000 residents (%). He estimates the following model as Ys ?? + ?| Education + ?2 Income + ?3 Mortality + ?. The following ANOVA table shows a portion of the regression results. df MS Regression Residual 417.3 139.1 94.6 47 50 69.1 486.4 Total Coefficients Standard Error t-stat p-value Intercept Education Income Mortality 4.8 12.471.65E-16 60.3 0.43 0 .05-7.78 5.45E-1 .75 6.02E-1 -0.20 0.08 0.03 0.17 0.4 0.6438 Which of the following is the value of the mean square error, (MSE)? r a. 0 b. 1.5 c. 3.0 d. 4.5 VOExplanation / Answer
1
The mse is given as
69.1/47 = 1.47 = 1.5 approx hence b
2
r2 is given as
1- SSres/SSTotal
= 1- 15.6/226.5= 0.9311
hence d
3
the regression equaiton is formed using the coefficients as
y = -1.6 -0.5*x1 +0.1x2
putting the values for x1 nad x2
y = -1.6 -0.5*1 +0.1*2
=-1.9
hence a
4
coffecient of determintation explains the variation
hence we calculate it as
1- SSres/SSTotal
= 1- 39375/220145= 0.8211 , which is 82% in percentage terms
hence d
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