Answer to Question #249838 in Macroeconomics for Hani

Question

a)      Use the p value approach to find out whether energy contributes negatively to mineral exploitation at the 5% level. Hint: specify the 5+1 steps. (6 marks)

 

b)     Use formula in Appendix to calculate adjusted R². (2 mark)

 

c)      What does adjusted R-squared imply? (2 marks)

 

d)     Interpret the coefficient on ln(energy). (2 marks)

 

e)      Are coefficients’ signs on explanatory variables within your expectation? Answer this question with a brief explanation. (9 Marks)

 

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f)      The researcher suspect that export and energy are jointly insignificant. Describe step-by-step procedure the researcher should carry out to determine if the variables are jointly insignificant.  (5 Marks)

Answer 1

a

Here H₀: energy contributed positively to mineral exploitation. H₁: energy contributed negatively to mineral exploitation.

After performing the test the p value is found to be 0.017 which is less than t-stat 2.49. Hence the test is significant and it can be concluded at 5% level of significance that energy contributed positively to mineral exploitation.

b

Adjusted $R^2= 1−\frac{(1−R^2)(N−1)}{N−K−1}$ where k is the number of independent variable

=0.8805

c.

The adjusted R² is very high which implies that all the independent variables has positive contribution in making the model better.

d.

The intercept of ln(energy) is -0.09 which implies that with with 0.09 unit decrease in energy there will 1 unit increase in ln(mining).

e.

The sign of ln(GDP_M) and ln(export) is as expected that is with increase in these two ln(mining) will increase. However, the sign of the coefficient of ln(energy) is negative which is quite surprising. there should be increase in mining with the consumption of energy.

f,

For testing if export and energy are insignificant the researcher has to perform F-test where the null hypothesis  

$H0: βexport=βenergy=0$

The test statistics $F_{q,n−k}=\frac{\frac{(RSS_R – RSSUR)}{q} }{\frac{RSS_{UR}}{(n−k)}}$

RSS_UR = Residual sum of squares, unrestricted

q = number of restrictions (here, the number of variables set equal to zero)

RSS_R = Residual sum of squares, restricted

k = number of variables in the regression, including the constant 

N = population size

If the computed value exceeds the critical value the null hypothesis should be rejected and hence it can be concluded that the the 2 variables are statistically significant.