Figure:
Suppose you regress the number of medals won by countries in the 1996,2000,2004,and 2008 Olympics on GDP Per Capita (Thousands) ,Population (Millions) ,and Olympic Year and that you get the results in Figure 6.1.

$\begin{array}{lc}\text { SUMMARY OUTPUT }\\\\\\\hline \text { Regression Statisties } & \\\hline \text { Multiple R } & 0.473932054 \\\text { R Square } & 0.224611592 \\\text { Adyasted R Square } & 0.218853757 \\\text { Standerd Error } & 14.85665558 \\\text { Observations } & 408 \\\hline\end{array}$

$\begin{array}{lccccc} \text { ANOVA }\\\hline & \text { ff } & S S & M S & F & \text { Sigejficance F } \\\hline \text { Regressice } & 3 & 25830.70959 & 8610.236529 & 39.00973242 & 3.69997 E-22 \\\text { Residual } & 404 & 89170.96688 & 220.7202151 & \\\text { Total } & 407 & 115001.6765 & & \\\hline\end{array}$

$\begin{array}{lcccccc}\hline & \text { Coefficients } & \text { Standand Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 385.4384477 & 338.9966744 & 1.136997725 & 0.25621316 & -280.9792491 & 1051.856144 \\\text { GDP Per Capita (Thousands) } & 0.28651666 & 0.046941033 & 6.103756974 & 2.4315 \mathrm{E}-09 & 0.194237479 & 0.37879584 \\\text { Popplasion (Milions) } & 0.041979674 & 0.00443387 & 9.467954334 & 2.42102 \mathrm{E}-19 & 0.033263338 & 0.050696011 \\\text { Year } & -0.191084928 & 0.169402339 & -1.127994491 & 0.259991678 & -0.524105098 & 0.141935242 \\\hline\end{array}$

$\text { Figure } 6.1$
-Based on the estimates in Figure 6.1,you should conclude that,holding all other independent variables constant,Olympic Year is estimated to have

Question

Figure:
Suppose you regress the number of medals won by countries in the 1996,2000,2004,and 2008 Olympics on GDP Per Capita (Thousands),Population (Millions),and Olympic Year and that you get the results in Figure 6.1.

$\begin{array}{lc}

\text { SUMMARY OUTPUT }\
\
\
\hline \text { Regression Statisties } & \
\hline \text { Multiple R } & 0.473932054 \
\text { R Square } & 0.224611592 \
\text { Adyasted R Square } & 0.218853757 \
\text { Standerd Error } & 14.85665558 \
\text { Observations } & 408 \
\hline
\end{array}$

$\begin{array}{lccccc}
 \text { ANOVA }\
\hline & \text { ff } & S S & M S & F & \text { Sigejficance F } \
\hline \text { Regressice } & 3 & 25830.70959 & 8610.236529 & 39.00973242 & 3.69997 E-22 \
\text { Residual } & 404 & 89170.96688 & 220.7202151 & \
\text { Total } & 407 & 115001.6765 & & \
\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text { Standand Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 385.4384477 & 338.9966744 & 1.136997725 & 0.25621316 & -280.9792491 & 1051.856144 \
\text { GDP Per Capita (Thousands) } & 0.28651666 & 0.046941033 & 6.103756974 & 2.4315 \mathrm{E}-09 & 0.194237479 & 0.37879584 \
\text { Popplasion (Milions) } & 0.041979674 & 0.00443387 & 9.467954334 & 2.42102 \mathrm{E}-19 & 0.033263338 & 0.050696011 \
\text { Year } & -0.191084928 & 0.169402339 & -1.127994491 & 0.259991678 & -0.524105098 & 0.141935242 \
\hline
\end{array}$

$\text { Figure } 6.1$
-Based on the estimates in Figure 6.1,you should conclude that,holding all other independent variables constant,Olympic Year is estimated to have
A)a statistically significant positive effect on Total Medals Won because -1.128 < .05.
B)a statistically insignificant positive effect on Total Medals Won because |-1.128| > .05.
C)a statistically significant positive effect on Total Medals Won because |-1.128| < 1.96.
D)a statistically insignificant positive effect on Total Medals Won because |-1.128| < 1.96.

Quizplus · Accepted Answer

The coefficient for Olympic Year is -0.1911, with a p-value of 0.260, which is greater than the level of significance 0.05. As the p-value is greater than the level of significance, we fail to reject the null hypothesis, which means that Olympic Year has no statistically significant effect on Total Medals Won once GDP Per Capita and Population are held constant. Therefore, the correct option should be D, which implies that Olympic Year has a statistically insignificant positive effect on Total Medals Won. Also, the value of |-1.128| is greater than 1.96, indicating that the coefficient of Olympic Year is not statistically significant at a 95% confidence interval.

Figure: Suppose You Regress the Number of Medals Won by Countries

Figure:
Suppose You Regress the Number of Medals Won by Countries