Question

3) Using x represent tax rate, y Gini index, and z GDP growth, find the least square regression lines y=a_0+a_1 x and z=b_0+b_1 x based on the following information (i.e. calculate the coefficients a_0, a_1, b_0 and b_1). Mean S.D. Tax Rate (x) 36.51 7.94 Gini Index (y) 0.31 0.04 GDP Growth (z) 2.01 0.76 4) Do the regression lines imply causal relationships? (i.e. will tax rate increase inevitably lead inequality or GDP growth to change?) Do your findings support the proposal to increase tax rate?

Answer 1

3).

For gini ~ tax rate, y = 0.485 -0.0047x

for GDP ~ tax rate, z = 1.69 +0.0075x

4).

The regression, Gini ~ Tax rate imply casual linear relationship

However, GDP ~ Tax does not as r_2 = 0.07 only

or we can say that tax rate can be increased as will only bring out 0.75 % change in Gini or inequality over 100% tax change but reverse can bring out huge changes.

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