ECO220Y1 Final: ECO220Y1Y UTSG Final Exam220 APR17 Solution
ECO220Y1Y, APRIL 2017, FINAL EXAM: SOLUTIONS
(1) Define the random variable to be a student’s percentile result. ~[0,100] and []=
=
=50 and
[]=()
=()
=833.33 and []=√833.33=28.87.
Given that the population is not too far from Normal (it is Uniform), a sample size of 38 is certainly sufficiently large to
employ the Central Limit Theorem: the distribution of
will be Normal even though is not.
Hence,
~(50,21.93) with [
]=[]=50 and [
]=[]
=.
=21.93 and [
]=√21.93=4.683.
(
>64)=>
.=(>2.99)=0.5−0.4986=0.0014 (Note: It does not matter if the inequality is
written as a strong or weak inequality because X-bar is a continuous random variable.)
(2) (a) Start with the intercept coefficient of 9.818475368: According to the OLS line, in June 2005 the predicted price of
a Big Mac hamburger is 9.82 Chinese Yuan (which is a bit below the actual price of 10.50 Chinese Yuan). Next, the slope
coefficient of 0.06467537: On average the price of a Big Mac hamburger in China has gone up by 0.065 Chinese Yuan per
month during the period from June 2005 and January 2017.
(b)
=9.82+0.78 with the unchanged at 0.98. The results show that prices on average are increasing by 0.065 ¥
per month, so that means they are increasing by 0.78 ¥ per year: the coefficient on t would be 0.78 if t were measured in
years. The constant term is unaffected because zero years is the same a zero months since June 2005. The is a unit-
free statistic and it would not be affected by a change in the units of measurement of the x-variable from months to
years (or any other change in the units of measurement of the x-variable and/or the y-variable).
(c) The number 4.30887E-17 is the P-value for the test of the overall statistical significance of the model and it is
extremely tiny indicating an extremely statistically significant result. This is not surprising because the R-squared is near
perfect: there is very little scatter and the price is rising steadily in a linear fashion. Hence, these data allow us to
decisively reject the possibility that Big Mac prices have been constant (not rising) during this period in China.
(d) Yes, that would clearly create a significant outlier: that would be nearly double the price in the earliest time period
and would substantially affect the OLS results as it bucks the trend of increasing prices over time (as prices are much
lower than 19.50 in the next time periods). The number 0.448771056 is a measure of the standard deviation of the
residuals (also called the Root MSE or ) and it would increase substantially with this outlier. The is measured in the
same units as the y-variable, which is Chinese Yuan, and it measures the amount of scatter around the OLS line: the
outlier would greatly increase the amount of scatter. Relative to the double-digit prices of Big Macs – ranging from 10.50
¥ to 19.60 ¥ – 0.45 ¥ is quite small amount of scatter, which is consistent with the very high R-squared values reported.
64.000
0
.05
.1
Density
36
40.6
45.3
50
54.7
59.4
64
X-bar
Sampling Distribution of Sample Mean
n = 38, mu = 50, sigma/root(n) = 4.683
P(X-bar > 60) = 0.00140
27
ECO220Y1 Full Course Notes
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