Question 3, 20 points. About 15 minutes You have n -28 quarterly observations on
ID: 3360866 • Letter: Q
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Question 3, 20 points. About 15 minutes You have n -28 quarterly observations on the imports M of a country, an index of import price PM , and real aggregate income GDP. Adding dummy variables 02, 03, and Q4 for Ridw ilr. the 2d, 3rd, and 4th of the year you estimate the model and find the following estimates along with their standard erors: logM 4.30-0.58 log P M + 1.45 logGDP + 0.15 Q2 + 0.10 Q3 + 0.40 Q4 0.253. n-28 (0.08) (0.13) (0.21) (0.10) (0.05) (0.12) (i) (10 points) Construct a 90% confidence interval for -Be sure to state precisely the degrees of freedom, t-values, etc. that you use to construct the confidence interval. There is no need to calculate the actual numbers, but do include enough information so the grader could use a calculator to construct the confidence interval (e.g., [7.5*1.88- 6.3]). See the attached table. Be sure to state what each number refers to. (ii) (5 points) Interpret the estimate of B (ii) (5 points) Give a precise "probabilistic" interpretation of what a 90% confidence interval means.Explanation / Answer
Answer to part (i)
Formula of confidence interval :
Slope - t * Standard error , Slope + t* Standard error
We got slope = 0.58
Standard error = 0.13
The T critical value will be for : Confidence level = 90%
df = n -1 = 28 -2 = 26
We can find the T critical value from the T table : 1.706
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On plugging the values we get:
0.58 - 1.706 * 0.13 , 0.58 + 1.706 * 0.13
0.58 -0.2218 , 0.58 + 0.2218
0.3582 , 0.8018
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Answer to part (ii)
Interpretation of slope of Quarter 3 (Beta 4)
The value of Beta 4 is 0.10, this implies that if there is a unit change in the Quarter 3 value , there would be an increase in the imports M by 0.10 times of the increase in the third Quarter value.
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Answer to part (iii)
The interpretation of 90% confidence interval is:
"There is 90% chances for the true value of slope to lie in the range "Lower limit - upper limit"
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In terms of the calculations in part (i) , the interpretation is as follows:
"there is 90% chances for the true value of slope Beta 1 to lie in the range 0.3582 and 0.8018"
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