Question

In: Math

3. Load the dataset called ec122a.csv and decide the appropriate regression to run. Write down what...

3. Load the dataset called ec122a.csv and decide the appropriate regression to run. Write down what transformations, corrections, etc... you make and why.

y1	x1
5.3478787576716	-0.930542577578737
-69.4411002445282	-14.3360876802962
17.6647698924475	1.81741420842464
98.6511466667161	16.8769469917607
14.7965900933862	1.44147861051093
-34.5302655286703	-8.00737844994315
93.0899709372717	15.9601981407006
9.21693205816442	0.677367144474178
82.6007511115692	13.940352476942
115.798113882096	21.2544523041556
210.387049747658	38.2407928740359
25.53810654411	2.87106608048978
103.832140647001	18.1287219709914
69.9887102526973	11.9894172917371
115.53192498448	20.8016798770016
121.344292025264	22.0189019228638
92.7341812552436	15.9508245127554
141.336831165046	25.3838968113616
43.9676084746945	6.62783843142594
170.312498248916	30.6056891002234
100.141722965535	18.0744156617512
135.127526516403	25.1557427275658
35.4910615569294	5.34067840867235
49.0886162426323	7.66630180243485
183.23305880313	33.6747888141339
133.899669788226	31.0484776835843
119.472386558899	19.6774321421239
158.382012262513	38.7948124929967
158.265751170527	32.3449530783571
143.893438668698	31.318399069747
209.554152576129	39.0470592670422
269.696741210151	47.0260908373683
214.277835307116	39.4621037661542
137.448728114245	32.1951502465506
207.142331867495	30.4353133960267
195.530279391204	37.8895119687649
260.613365801387	47.5777648932458
193.358564414283	32.544387671943
214.355032319599	35.3968738633248
236.246295426679	46.8573949752216
179.510295035057	40.1659721878024
212.202997184581	42.9660084481672
207.263001917022	38.3563234239438
189.537080855405	36.9994190965688
293.77520107103	52.1838828310905
275.816868619373	46.9729303988204
213.777730095761	51.623410535034
234.515710668196	54.7713564277226
305.755164538293	58.2281799071355
247.574028943277	48.2612135595578
216.487201880791	44.4805702248886
298.939398951728	59.5098240982159
294.087515977881	59.7323992058337
242.47071086964	56.2423387201774
314.216664214321	52.099463290858
198.64183568504	45.5524703388986
451.501739075897	71.7371279051027
334.639764748968	56.3003387632005
325.539711644784	61.3753202076771
334.360999254428	65.6509595487347
375.501692057963	69.0188962996762
279.92394271145	50.820033316856
391.747159079897	84.4387655124175
256.755426083081	61.8425207887276
335.348364682454	78.2972291401232
326.862654481865	67.2701863797509
409.199061682728	67.0226394402898
315.278602307445	62.6960929012151
389.115799067651	67.3988546408951
324.558498258645	74.4613819502999
277.860262868103	51.1152020598209
348.220952805656	73.4318499899927
394.101591698092	69.6828387504708
378.574744964529	70.3390300051774
345.129291309579	65.1443486887627
431.388383747861	86.5385881418601
461.246340384882	80.7778216315798
393.128587286873	79.4875434916298
457.413617158369	93.3535591485397
490.030080973679	86.1469790728216
445.013611790392	88.2858459293727
502.433226880918	90.1840214865989
531.919402102633	84.5845337879384
459.430685958911	101.584476353668
524.534588061157	93.7218122436017
384.831820262549	88.3997031202485
369.255646051443	64.059370789963
460.011550161416	94.6172825629485
581.849448405881	100.291462036955
487.238487436963	86.277129080676
554.389543790077	106.054358170647
476.138213629779	77.2218509347784
360.434234419891	84.2953663204438
497.064285198229	98.5692172324988
559.620017287958	104.394884303588
570.274724422607	113.867023345632
526.006391282654	110.550311578395
668.85329391523	118.103935026271
567.23894595309	105.330310697067
551.525236136496	104.258750461435

Expert Solution

Let's use excel:

Simple linear regression using Excel.

Step 1) First enter the given data set in excel columns.

Step 2) Then click on Data >>> Data Analysis >>>Regression >>>>OK

Step 3) Input Y Range: Select the data of column "A"

Input X Range: Select the data of column "B"

Click on Lable

then Click on Ouput Range

Select the box "Residual plot"

Look the following Image

Then Click on OK, so we get following result.

From the above output the Correlation = R = 0979733

Even though the correlation between y1 and x1 is very hight the ordinary least square estimators are misleading. Because the assumption of constant variance of the residual is violated.

From the residual plot, we conclude that as the level of x1 increases the variance of the residuals also increases.

So we need to used transformation.

The transformation here such that the weight of the small values of x is greater than the weight of the larger vaues of X.

milcah answered 6 months ago

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