Question

SECTION 9.3 Measures of Regression and Prediction Intervals 505 12.)Earnings of Men and Women The table shows the median annual earnings (in dollars) of male and female workers from 10states in a recent year. The equation of the regression line is 1.005x 10,770.313. Source .S. Census Burean) Median annual earnings so.976 46,763 46,934 of male workers, r Median annual earg 40.214 36.834 36,841 31 110 40.173 of female workers, y Median annual earnings of male workers, x 47.092 51.628 46.123 61.66 43.829 Median anual earnings 32,096 35,753 41,690 3,443 $0.802

Answer 1

• Here let X be the independent variable denoting the median annual income of male and Y be the dependent variable denoting the median annual income female.
• To find the coefficient of determination we will find first find the sum of squares of variables annual income of male and female .is X and Y
• $ssx=\sum x^{2}-n\bar{x}^{2}$=23710959939.00-(10*48406.30²)=279261142.10
• $ssy=\sum y^{2}-n\bar{y}^{2}$=14658634440.0-(10*37895.6²)=297869446.4

• $ssxy=\sum xy-n\bar{x}\bar{y}$=18624616701-(10*48406.30*37895.6)=280758878.2

• The coefficient of determination is given by

• $R^{2}=\frac{SSxy^{2}}{SSxx*SSyy}$

• substituting the respective values coefficient of determination is

• 0.9476=94.76%
  

• The value of coefficient of determination we can say that 94.76% of the data is explained by the model

• The overall standard error is given by

• $\hat{\sigma }=\sqrt{\frac{1}{n-2}(SSyy-\frac{SSxy^{2}}{SSxx})}$

• =1396.638

• The standard error is very high of the data, which can give us the biased result