The Organisation for Economic Co-operation and Development collects data on Main
ID: 3023801 • Letter: T
Question
The Organisation for Economic Co-operation and Development collects data on Main Economic Indicators (MEIs) for many countries. Each variable is recorded as an index with the year 2000 serving as a base year. This means that the variable for each year is reported as a ratio of the value for the year divided by the value for 2000. Use of indices in this way makes it easier to compare values for different countries.
The following table gives the values of three MEIs for 21 countries:
What is the predicted value of production for a country that has an index of 160 for dwelling permits? (Use decimal notation. Give your answer with tolerance = ±1.)
Predicted value of production = .
The country with ID = 15 has an index of 160 for dwelling permits. Find the residual for this country. Residual is actual value minus predicted value. (Use decimal notation. Give your answer with tolerance = ±1.) Residual =
Country ID Dwelling permits sales production 2 113 136 108 2 121 102 107 3 220 117 98 4 174 139 163 5 120 126 108 6 105 137 126 7 140 121 105 8 51 105 118 9 119 138 103 10 111 141 159 11 97 123 143 12 82 104 110 13 158 113 151 14 141 161 118 15 160 108 111 16 123 139 109 17 120 137 91 18 163 142 160 19 51 110 105 20 119 122 109Explanation / Answer
a. Here, data is provided for 20 countries, as opposed to 21, as mentioned in the question. We run a simple regression of the production figures (the explained variable) using the dwelling permits figures as the explanatory variable.
Note: Since the question mentions only the dwelling permits figure, the sales figure has not been included as a regressor.
The results of the regression have been shown below. Here, MS Excel has been used to perform the regression. However, the regression can be done using any statistical software package.
Without the availability of a software package, the formulae for the intercept and slope coefficient are as follows:
Slope Coefficient, b = [ xy - x y / n ] / [ x2 – ( x)2 / n ]
Intercept Coefficient, a = Mean (y) – b * Mean (x)
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
107.8841
16.9346
6.370635
5.32E-06
72.30588
143.4624
72.30588
143.4624
X Variable 1
0.098198
0.129953
0.755645
0.459637
-0.17482
0.371219
-0.17482
0.371219
Therefore, using the intercept coefficient of 107.8841 and slope coefficient of 0.098198, the predicted value of production for a country that has an index of 160 for dwelling permits is:
Predicted Value = 107.8841 + 0.098198 * 160
= 123.60
b. Therefore, Residual = Actual Value – Predicted Value
= 111.0 - 123.60
= -12.60
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
107.8841
16.9346
6.370635
5.32E-06
72.30588
143.4624
72.30588
143.4624
X Variable 1
0.098198
0.129953
0.755645
0.459637
-0.17482
0.371219
-0.17482
0.371219
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