Suppose That You Regress the Total Number of Medals That

question 20

Essay

Suppose that 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 Figure 4.2. SUMMARY OUTPUT

$\begin{array}{lc}\hline \text { Regression Statistics } & \\\hline \text { Mutiple R } & 0.193666659 \\\text { R Square } & 0.037506775 \\\text { Adjusted R Square } & 0.027881842 \\\text { Standard Error } & 17.8035921 \\\text { Observations } & 102 \\\hline\end{array}$

$\begin{array}{l}\text { ANOVA }\\\begin{array}{lccccc}\hline & \text { if } & S S & \text { MS } & F & \text { Significance } F \\\hline \text { Regression } & 1 & 1235.171633 & 1235.171633 & 3.896835188 & 0.05113579 \\\text { Residual } & 100 & 31696.78915 & 316.9678915 & & \\\text { Total } & 101 & 32931.96078 & & & \\\hline\end{array}\end{array}$

$\begin{array}{lcccccc}\hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper } 95 \% \\\hline \text { Intercept } & 6.0792 & 2.3079 & 2.6341 & 0.0098 & 1.5005 & 10.6580 \\\text { GDP Per Capita (Thousands) } & 0.1553 & 0.0787 & 1.9740 & 0.0511 & -0.0008 & 0.3113 \\\hline\end{array}$
Figure $4.2$
How would you interpret these results? What would you say about the Goodness-of-Fit of the regression? Explain.
What would be the predicted number of medals for a country with a GDP per capita of $25,000? $40,000? Show your work.