First Nar Analysis Questions. Please show all work 1. Suppose that Last Name: yo
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First Nar Analysis Questions. Please show all work 1. Suppose that Last Name: you regress the total number of medals that a country won in the 2008 Olympics on GDP per capita and that you get the results in the Figure below SUMMARY OUTPUT Regression Multiple R R Squme Adjusted R Square Standard Error Observations 0 193666659 0.037506775 0.027881842 17.8035921 102 ANOVA Significance F MS Regression 1235.171633 1235.171633 3.896835188 0.05113579 100 31696.78915 316.9678915 101 Total 32931 96078 Upper 9596 P-value Lower 95% Stat0.0098 2.6341 19740 10.6580 0.3113 Coefficients Starndard ErrorStat 1.5005 0.0008 60792 GDP Per Capita (CThousands) 0.1553 2.3079 0.0787 0.0511 How would you interpret these results? What would you say about the Goodness-of-Fit of the regression? Explain. a) What would be the predicted number of medals for a country with a GDP per capita of $25,000? $40,000? Show your work. b)Explanation / Answer
a) The value of R square in the regression output is the most commonly used measure to determine the goodness of fit of the regression. The value of R square varies between 0 and 1 and closer it is to one, the better the goodness of fit. From the regression output, the value of R square is 0.0375 which indicates a poor goodness of fit.
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b) The general form of regression line is
y = b0 +b1 X
where b0 = intercept and b1 is the slope
y = 6.0792 + 0.1553 X
Predicted number of medals with GDP per capita of $ 25,000 = 6.0792 + 0.1553 * $ 25,000
Predicted number of medals with GDP per capita of $ 25,000 = 3838.58
Predicted number of medals with GDP per capita of $40,000 = 6.0792 + 0.1553 * 40,000
Predicted number of medals with GDP per capita of $40,000 = 6138.08
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