1. The government of Jamaica would like to estimate a model that explains the de
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Question
1. The government of Jamaica would like to estimate a model that explains the
determinants of imports. The following model with its associated variables is proposed by the
Minstry of Finance.
Where
Mt=Imports
Yt=Income
Cg=Government expenditure
Ratiot=ratio of foreign prices to domestic prices
Boomt=Dummy variable representing the boom years from 1974 to 1981
Model 8: OLS, using observations 1967-1991 (T=25)
Dependent variable:m
Coefficient std. error t-ratio p-value
Const -759.871 1232.98 -0.6163 0.5447
y 0.405342 0.114016 3.555 0.0020 ***
cg -0.173065 0.552459 -0.3133 0.7573
ratio -891.753 579.847 -1.538 0.1397
boom 43.9133 225.114 0.1951 0.8473
Mean dependent var 3556.082 S.D. dependent var 1531.723
Sum squared resid 3198563 S.E. of regression 399.9102
R-squared 0.943195 Adjusted R-squared 0.931835
F(4, 20) 83.02109 P-value (F) 3.65e-12
Log-liklihood -182.4652 Akaike criterion 374.9303
Schwarz criterion 381.0247 Hannan-Quinn 376.6207
rho 0.129536 Durbin-Watson 1.728300
Excluding the constant, p-value was highest for variable 12 (boom)
a. Name four assumptions that guide the estimation of a OLS regression model.
b. Use the results of the estimated regression model to answer the following questions:
i. Write down the OLS regression estimated equation.
ii. Is the overall regression model statistically significant? Prove your answer.
iii. Which variables of the model are statistically significant?
iv. What is the value of the R2. What is the Interpretation of the value of this R2?
Alt = 30 + 31Yt + 32cg + 33/. at iot + 34Boomt + EtExplanation / Answer
a) Assumptions for OLS regression are as follows:
Linearity - the dependent variable is linearly related to the independent variable
Independence - The Yi values are independent of each other
Normality - The residual values hosuld be normally distributed with a mean of 0.
Homoscedasticity - The variance of the dependent variable should not vary with the levels of the independent variable. The residuals should have constant variance.
b) 1) OLS regression estimated quation is as follows:
Mt = -759.871 + 0.405342 Yt - 0.173065 cg - 891.753 ratiot + 43.9133 boomt
2) Yes, the overall regression model is statistically significant as the P value associated with F statistic is very small.
3) The variables for which p value is less that the usual cut off of 0.05 can be termed as statsitically significant. In this case Yt i.e. Income variable
4) The value of R2 is 0.943195. R2 value tells us the percentage of variance explained by the model.
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