Question

8. A politician feels Tax Revenues (TR) are a function of Consumer Incomes (Cl). Data collecte or several taxpayers are shown below. Estimate and interpret the regression model. CIRCLE YOUR ANSWERS USE THE TABLE BELOW TO ORGANIZE YOUR COMPUTATIONS Tax Consumer Revenues(Y)Income (x) Fred Sam Jane Mary Paul Al Jenny Don Bob 61 43 43 39 15 25 20 10 51 46 43 41 43 42 12 6 9. Given the values from the previous problem calculate and interpret the standard error of the cstimate. Use a graph to illustrate and explain how it can he used as a mcasure of goodness of fit. 10. Based on the data above for taxes and incomes, test the significance of the regression coefficient at the 5% level. Clearly show all four steps, what is the p-value associated with the test?

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61 39 15 25 20 2379 645 1075 1020 1521 625 400 100 25 144 36 3721 1849 1849 2601 2116 1849 1681 1849 1764 19279 43 51 46 43 215 492 258 126 6670 12 43 42 413 Sum- 135 Based on the above table, the following is calculated: に1 Y-413 ー Y; 45.888888888889 i=1 ssxx ΣΧ-1 (ΣΧ.) 3085-1352/9-1060 ss,γ = ΣΥ-n SY; ) = 19279-4132/9 326.88888888889 Y. 1-6670-135 x 413/9-475 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows 772 475 SSxx 1060 0.4481 n = Y-X . m 45.888888888889-15 × 0.4481-39-1672 Therefore, we find that the regression equation is Y = 39.1672 +0.4481x

Y^= 39.1672 + 0.4481

slope -

when consumer income increases by 1 unit , tax revenue increases by 0.4481 unit

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