1. A. Quarterly data from 2013 to 2016 produced this estimate of a linear trend
ID: 3172954 • Letter: 1
Question
1. A. Quarterly data from 2013 to 2016 produced this estimate of a linear trend model for gasoline sales (St) across time:
St = 22,902.05 + 117.06t R2 = 0.48
(10.75)
where the number in parenthesis under the estimated coefficient is the t-statistic. Use these regression results to forecast sales for the first quarter of 2017.
B. Using the same set of data, the estimate of an exponential trend model is
lnSt = 10.04 + 0 .0049t R2 = 0.41
(3.15)
Use these regression results to forecast sales for the first quarter of 2017.
C. Which form for the trend fits the data better? (Assess their t-statistic and R2 values.) Also, why might we expect both of them to give poor results?
Explanation / Answer
A. Let the t varies as 0,1,2,3,4 for the quarterky data in the year 2013,2014,2015,2016,2017.
Regression equation is St = 22,902.05 + 117.06t
So, t= 4 for year 2017.
St = 22902.05 + 117.06 * 4 = 23370.29
B. Regression equation is lnSt = 10.04 + 0 .0049t
So, t= 4 for year 2017.
ln(St) = 10.04 + 0.0049 * 4 = 10.0596
St = antilog(10.0596) = 23379.15
C. R-squared of the 1st equation is 0.48
R-squared of the 2nd equation is 0.41
t-statistic of the 1st equation is 10.75
t-statistic of the 2nd equation is 3.15
As, the R-squared and t-statistic of the 1st equation is greater than the R-squared and t-statistic of the 2nd equation, 1st euation (linear trend model) fits the data better.
But both have low R-squared and t-statistic, so both might give poor results. High R-squared shows that the high percent of variation in the “dependent” variable has been explained by the model. The t-statistic is the ratio of the estimate divided by the standard error. So, high t-statistic shows that the estimate is stable and the standard error is low.
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