Regression Models using Cross Section Data Assignment 2022

MAE256 T2 2019 – Assignment Details
Student Name:
University Name:
27th July 2019

Regression Models using Cross Section Data
v) Now re-estimate the equation in (iv) but using the log of independent variables.
That is, estimate the model,
TotalMedals=β0+ β1log(realGDP)+ β2log(population)+u
Report the results in a sample regression function. Interpret the coefficient of
population? Test whether it is statistically significant at 1% level.
Answer
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.480379
R Square 0.230764
Adjusted R Square 0.229534
Standard Error 14.19632
Observations 1254
ANOVA
df SS MS F
Significance
F
Regressio
n 2 75633.92 37816.96 187.6441 5.38E-72
Residual 1251 252121 201.5356
Total 1253 327755
Coefficient
s
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Intercept -27.3506 2.160388 -12.66 1.19E-34 -31.5889 -23.1122
LogRealGDP 8.02186 0.605008 13.25909 1.22E-37 6.834917 9.208803
LogPop -0.14135 0.669908 -0.21101 0.832918 -1.45562 1.172913
From the above results, we have the regression equation as follows;
TotalMedals=−27.3506+8.0219 log ( realGDP ) −0.1414 log (population)
The coefficient of log(population) is given as -0.1414; this implies that a 1%
increase in the population is expected to result in a decrease in the total medals
by 0.0014. Similarly, a 1% decrease in the population is expected to result in an
increase in the total medals by 0.0014.
Looking at the significance of the population variable, it can be seen that the
variable is insignificant at 1% level of significance (p > 0.01).
vi) Using the estimated model in (v), test whether realGDP has a positive effect on
total medals at 1% level of significance.
Answer
From the above results, it can be seen that the realGDP is significant in the
model at 1% level of significance. The coefficient of the log(realGDP) is
8.0219; this implies that a 1% increase in the real GDP is expected to result in