Suppose you have cross-section data on income (y) and electricity consumption (x) for three regions and you have regressed ln x on an intercept and ln y for each region and for the full sample, obtaining the following results:
Estimated Intercept Std Error. Slope Std. Error SSE n
Region A 0.02 0.008 1.10 0.05 48 92
Region B 0.01 0.003 0.90 0.1 35 82
Region C 0.015 0.001 0.85 0.08 17 32
All regions0.03 0.0015 0.88 0.05 112 206
a. Test (at the 5% level) that this equation is the same for all regions.
b. Assuming that these equations are the same (regardless of your answer to (a)), test (at the 5% level) that the common income elasticity is 1.
c. Suppose you know that the intercepts are definitely different for all three regions. Explain what you would do to answer parts (a) and (b) given this knowledge (i.e. outline any changes in estimation and inference relative to your previous answers).
Step by step method for computing regression model s given in the answer.