The following model can be used to study whether campaign expenditures affect...
The following model can be used to study whether campaign expenditures affect election outcomes:voteA 5 b 0 1 b 1 log( expendA ) 1 b 2 log( expendB ) 1 b 3 prtystrA 1 u ,where voteA is the percentage of the vote received by Candidate A, expendA and expendB are campaign expenditures by Candidates A and b, and prtystrA is a measure of party strength for Candidate A (the percentage of the most recent presidential vote that went to A’s party).[*]What is the interpretation of b 1 ?
[*]In terms of the parameters, state the null hypothesis that a 1% increase in A’s ex- penditures is offset by a 1% increase in b’s expenditures.
[*]Estimate the given model using the data in VOTE1.RAW and report the results in usual form. Do A’s expenditures affect the outcome? What about b’s expendi- tures? Can you use these results to test the hypothesis in part (ii)?
[*]Estimate a model that directly gives the t statistic for testing the hypothesis in part (ii). What do you conclude? (Use a two-sided alternative.)
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Considër the pravided détails and the rnode1 ta solve the subparts The rrïoôel to test tête relationship is given as beïop/:
(i) Holding other factors fîxed, the interpoJation of slope @ is w'rrlten as.
- (@ / l 00) 100 x A lög(W/›rud4)
.g,/100 I (céteris paribus) percentage point change in percentage of vote received when campaign expenditure 'by candidate A increases by one percent. It can aJso say that when campaign e?penditur.e by ñandidaté A:inoeases {deaeases) by 1 then pea rrtg Df Vote received will be inaeases {decreases) by @ percentages.
(ii)
The null hypothesis at 1% level of significance that increase in As expenditure is offset by a 1% increase in B's percent is given as below:
The above hypothesis indicate that a Z% increase in expenditure A and a Z% increase in expenditure B results percentage of vote received unchanged. The alternate hypothesis against the null hypothesis is given as below:
The above hypothesis indicate that a Z% increase in expenditure A and a Z% increase in expenditure B results percentage of vote received changed.
Consider 'the provided datà VOTE1.RÕ'/ to estimate the model. Let us consider /expend A, lexpend8 and prf fe as expIanatory.vanabIes artd voteA as dependem vanable. regressing valer on explanatory va'nabIe in the Minitab software is .as fóIIoa's.
1.. Write the provided deta irito Minitab worksheet.
[*]
Click on the stat option > Regression > Regression. a new dialog box will open. Now select the vateA as.respanse vafiâble. and the explanatory vañables as the predictors. The scréenshot is shown below: 3.Press OK bñtt”on in the above.dia1og box. The soeen Not is given as below: ” egredsion 1nalyeie: votsA versus Imxpen4A, Imxpen4B, prtyatrA
yocw- t9 .1+6 - 08sexpo - 6.”62 z›oxgeodo • 0. 15Z gccyacxs
Oonacanc45.0803.”926tt.460-000
xpaoaA‹.Oe3xD.3ezzOS.92o.O0ó
Z «paodB-6.615Ê”D.”37B8-II.460.000
.pWy•0rAO.151940.O€2D22.45O.015
# = 7.7123& R-5q = 79 3%R-Rq(adj) = 78.9$
Ragreszion388€05tt80t215.2B0-000
Raaidual &rtar1691005359
The regression model in the usuaJ form is given as delow. voieA -— (IN.1) + â.O8]og(6Tpe/zdd) - ii.62log(Wjseuz/8) + D.ISO (. ir2)
(It.48) (15.92) (—17.46) (2.41) The coefficient on Ioq{Erpenâd) is very significant {f. statistic is 15. 92), as is the coéfficient on \og(I statistic is —1?’.45”). The estimatés imply that a 10% lteris paribufi ”inl ease in spending by candidate A inoeases the predided share of the vote going to A by about .61 percentage poirits. Simñarly, a 1 0% ceteris paribus inoease in
spending by B reduces voteA ây about . 66 percentage points. These efiects certainly cannot be ignored. The coefficients on log(expend4) and log(expendB) are of opposite in sign. Hence there will needto test the hypothesis from part (ii).
(iv)
Recording to the part (iii) regression analysis, the p-value for the explanatory variables “log(expend4) and log(e endB)" is approximately 0. Thus, the P-value is approximately 0.0001. Now comparing the P-value with the level of significance (say 0.01). P-value (0.0017) is less than the level of significance (0. 01). so the null hypothesis is rejected and it is conduded that the sum of the slopes is greater than zero.
Mathematically the hypothesis of the par! (ii) can be whtten as d, = /t, + //, or @, = d, - //,
!• g9Ï •a ‹* ÏS into the original equat ion,and FOarranging 9Ï+
When estimate this equation, it obtain that • -.532 andt j §3 . The I statistic far
the hypothesis in part (ii) is —Q.$ $}ffi.¿$$ —\ . Therefore, null hypothesis does not get
rejected.
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