Eastern Electric Produces a 25-inch thin-walled television

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Sheet1

Eastern Electric Produces a 25-inch thin-walled television. The company wants to get a better grasph on the sensitivity of the qunatity demanded of its product to the various factors that affect it.You have been hired as a consultant to estimate the following demand function QE = β0 + β1PE + β2PG + β3I a. Find the estimated values for β0 β1 β2 β3 b. Which of the estimated values you found in part a. are significantly different from zero (one-tailed tests) at the 5% level of significance? Why? c. What is the value of R^2
Analysis of Full model QE = β0 + β1PE + β2PG + β3I,
Q = QTY of T.V price easter electric T.V price generally excellent T.V Avg. annual Household T.V
250 900 1400 30000
400 800 1500 30000
330 800 1200 30000
360 800 1200 32000
445 700 1200 32000
380 700 1000 31000
440 675 1000 32000
400 675 900 32000
450 630 900 32000
500 630 950 38000
440 630 800 38000
500 595 800 38000
470 595 750 38000
520 595 750 42000
480 595 700 42000
440 625 700 42000
410 625 700 39000
460 625 750 39000
7675 12195 17200 637000
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9806240008
R Square 0.9616234309
Adjusted R Square 0.9533998804
Standard Error 14.3946803604
Observations 18
ANOVA
df SS MS F Significance F
Regression 3 72689.3822602816 24229.7940867605 116.9353102064 0.0000000004
Residual 14 2900.8955174962 207.2068226783
Total 17 75590.2777777778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 786.8849493834 82.4563701235 9.5430461977 0.0000001662 610.0336249557 963.7362738112 610.0336249557 963.7362738112
price easter electirc T.V -1.2065076625 0.0950314902 -12.6958722813 0.0000000045 -1.410329937 -1.002685388 -1.410329937 -1.002685388
price generally excellent T.V 0.2926048047 0.0390148717 7.4998274299 0.0000028796 0.2089262276 0.3762833819 0.2089262276 0.3762833819
Avg. annual Household T.V 0.0050104069 0.0014149797 3.5409745133 0.003258821 0.0019755774 0.0080452365 0.0019755774 0.0080452365
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted QTY of T.V Residuals Standard Residuals Percentile QTY of T.V
1 260.9869876347 -10.9869876347 -0.8410795099 2.7777777778 250
2 410.8982343596 -10.8982343596 -0.8342852398 8.3333333333 330
3 323.116792938 6.883207062 0.5269255427 13.8888888889 360
4 333.1376067964 26.8623932036 2.0563788056 19.4444444444 380
5 453.7883730474 -8.7883730474 -0.6727704391 25 400
6 390.2570051704 -10.2570051704 -0.7851976509 30.5555555556 400
7 425.4301036624 14.5698963376 1.1153595215 36.1111111111 410
8 396.1696231885 3.8303768115 0.2932242721 41.6666666667 440
9 450.4624680014 -0.4624680014 -0.0354030033 47.2222222222 440
10 495.1551498136 4.8448501864 0.3708845732 52.7777777778 440
11 451.2644291028 -11.2644291028 -0.8623183009 58.3333333333 445
12 493.4921972906 6.5078027094 0.4981874646 63.8888888889 450
13 478.8619570537 -8.8619570537 -0.6784034663 69.4444444444 460
14 498.9035847705 21.0964152295 1.6149797534 75 470
15 484.2733445336 -4.2733445336 -0.3271344836 80.5555555556 480
16 448.0781146583 -8.0781146583 -0.6183985041 86.1111111111 500
17 433.0468938706 -23.0468938706 -1.7642934392 91.6666666667 500
18 447.6771341076 12.3228658924 0.9433441039 97.2222222222 520
7675
consider
QE = β0 + β1PE + β2PG
QTY of T.V price easter electirc T.V price generally excellent T.V
250 900 1400
400 800 1500
330 800 1200
360 800 1200
445 700 1200
380 700 1000
440 675 1000
400 675 900
450 630 900
500 630 950
440 630 800
500 595 800
470 595 750
520 595 750
480 595 700
440 625 700
410 625 700
460 625 750
7675 12195 17200
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9629398217
R Square 0.9272531001
Adjusted R Square 0.9175535135
Standard Error 19.1467288208
Observations 18
ANOVA
df SS MS F Significance F
Regression 2 70091.3194097372 35045.6597048686 95.597176845 0.0000000029
Residual 15 5498.9583680405 366.597224536
Total 17 75590.2777777778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1047.8535134775 49.1861445198 21.3038351289 0 943.0157285791 1152.6912983759 943.0157285791 1152.6912983759
price easter electirc T.V -1.2363975611 0.125904151 -9.8201493048 0.0000000634 -1.5047559053 -0.9680392168 -1.5047559053 -0.9680392168
price generally excellent T.V 0.2262502915 0.0455168819 4.9706896062 0.000167633 0.1292333548 0.3232672282 0.1292333548 0.3232672282
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted QTY of T.V Residuals Standard Residuals Percentile QTY of T.V
1 251.8461166828 -1.8461166828 -0.1026463218 2.7777777778 250
2 398.1109019425 1.8890980575 0.1050361383 8.3333333333 330
3 330.2358144804 -0.2358144804 -0.0131115705 13.8888888889 360
4 330.2358144804 29.7641855196 1.6549247371 19.4444444444 380
5 453.8755705861 -8.8755705861 -0.4934924663 25 400
6 408.625512278 -28.625512278 -1.5916131268 30.5555555556 400
7 439.5354513044 0.4645486956 0.0258294697 36.1111111111 410
8 416.9104221504 -16.9104221504 -0.9402399375 41.6666666667 440
9 472.548312398 -22.548312398 -1.2537134585 47.2222222222 440
10 483.860826975 16.139173025 0.8973575527 52.7777777778 440
11 449.9232832439 -9.9232832439 -0.5517465581 58.3333333333 445
12 493.1971978809 6.8028021191 0.3782440309 63.8888888889 450
13 481.8846833039 -11.8846833039 -0.6608027752 69.4444444444 460
14 481.8846833039 38.1153166961 2.1192577375 75 470
15 470.5721687269 9.4278312731 0.5241988289 80.5555555556 480
16 433.4802418952 6.5197581048 0.3625064412 86.1111111111 500
17 433.4802418952 -23.4802418952 -1.3055298664 91.6666666667 500
18 444.7927564722 15.2072435278 0.8455411448 97.2222222222 520
7675
consider
QE = β0 + β1PE
QTY of T.V price easter electirc T.V
250 900
400 800
330 800
360 800
445 700
380 700
440 675
400 675
450 630
500 630
440 630
500 595
470 595
520 595
480 595
440 625
410 625
460 625
7675 12195
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8985686363
R Square 0.8074255941
Adjusted R Square 0.7953896937
Standard Error 30.1628422426
Observations 18
ANOVA
df SS MS F Significance F
Regression 1 61033.5249433106 61033.5249433106 67.084768849 0.0000004081
Residual 16 14556.7528344671 909.7970521542
Total 17 75590.2777777778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 877.2566893424 55.5046551524 15.8051011565 0 759.5920775337 994.9213011512 759.5920775337 994.9213011512
price easter electirc T.V -0.6654875283 0.0812508582 -8.1905292167 0.0000004081 -0.8377316522 -0.4932434045 -0.8377316522 -0.4932434045
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted QTY of T.V Residuals Standard Residuals Percentile QTY of T.V
1 278.3179138322 -28.3179138322 -0.9677283468 2.7777777778 250
2 344.8666666667 55.1333333333 1.8841108789 8.3333333333 330
3 344.8666666667 -14.8666666667 -0.5080492454 13.8888888889 360
4 344.8666666667 15.1333333333 0.5171622364 19.4444444444 380
5 411.4154195011 33.5845804989 1.147709918 25 400
6 411.4154195011 -31.4154195011 -1.073581626 30.5555555556 400
7 428.0526077098 11.9473922902 0.4082867918 36.1111111111 410
8 428.0526077098 -28.0526077098 -0.9586618507 41.6666666667 440
9 457.9995464853 -7.9995464853 -0.2733742302 47.2222222222 440
10 457.9995464853 42.0004535147 1.4353115729 52.7777777778 440
11 457.9995464853 -17.9995464853 -0.6151113908 58.3333333333 445
12 481.2916099773 18.7083900227 0.6393352086 63.8888888889 450
13 481.2916099773 -11.2916099773 -0.3858762732 69.4444444444 460
14 481.2916099773 38.7083900227 1.3228095298 75 470
15 481.2916099773 -1.2916099773 -0.0441391126 80.5555555556 480
16 461.326984127 -21.326984127 -0.7288223 86.1111111111 500
17 461.326984127 -51.326984127 -1.7540337818 91.6666666667 500
18 461.326984127 -1.326984127 -0.0453479788 97.2222222222 520
7675
consider
QE = β0 + β2PG
QTY of T.V price generally excellent T.V
250 1400
400 1500
330 1200
360 1200
445 1200
380 1000
440 1000
400 900
450 900
500 950
440 800
500 800
470 750
520 750
480 700
440 700
410 700
460 750
7675 17200
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.6779097794
R Square 0.459561669
Adjusted R Square 0.4257842733
Standard Error 50.529622229
Observations 18
ANOVA
df SS MS F Significance F
Regression 1 34738.3942161339 34738.3942161339 13.6055980533 0.001989796
Residual 16 40851.8835616438 2553.2427226027
Total 17 75590.2777777778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 599.8287671233 48.5057084505 12.3661479501 0.0000000013 497.0012594186 702.656274828 497.0012594186 702.656274828
price generally excellent T.V -0.1815068493 0.0492078284 -3.6885766975 0.001989796 -0.2858227849 -0.0771909137 -0.2858227849 -0.0771909137
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted QTY of T.V Residuals Standard Residuals Percentile QTY of T.V
1 345.7191780822 -95.7191780822 -1.9526184059 2.7777777778 250
2 327.5684931507 72.4315068493 1.4775627651 8.3333333333 330
3 382.0205479452 -52.0205479452 -1.0611904682 13.8888888889 360
4 382.0205479452 -22.0205479452 -0.449207025 19.4444444444 380
5 382.0205479452 62.9794520548 1.2847460638 25 400
6 418.3219178082 -38.3219178082 -0.7817459736 30.5555555556 400
7 418.3219178082 21.6780821918 0.4422209127 36.1111111111 410
8 436.4726027397 -36.4726027397 -0.7440209668 41.6666666667 440
9 436.4726027397 13.5273972603 0.2759514384 47.2222222222 440
10 427.397260274 72.602739726 1.4810558213 52.7777777778 440
11 454.6232876712 -14.6232876712 -0.298306998 58.3333333333 445
12 454.6232876712 45.3767123288 0.9256598883 63.8888888889 450
13 463.698630137 6.301369863 0.1285444675 69.4444444444 460
14 463.698630137 56.301369863 1.1485168727 75 470
15 472.7739726027 7.2260273973 0.1474069709 80.5555555556 480
16 472.7739726027 -32.7739726027 -0.6685709533 86.1111111111 500
17 472.7739726027 -62.7739726027 -1.2805543964 91.6666666667 500
18 463.698630137 -3.698630137 -0.0754500135 97.2222222222 520
QE = β0 + β3I,
QTY of T.V Avg. annual Household T.V
250 30000
400 30000
330 30000
360 32000
445 32000
380 31000
440 32000
400 32000
450 32000
500 38000
440 38000
500 38000
470 38000
520 42000
480 42000
440 42000
410 39000
460 39000
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.7016817107
R Square 0.4923572232
Adjusted R Square 0.4606295497
Standard Error 48.9724785659
Observations 18
ANOVA
df SS MS F Significance F
Regression 1 37217.4192676486 37217.4192676486 15.5182264601 0.0011725534
Residual 16 38372.8585101292 2398.3036568831
Total 17 75590.2777777778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 60.5606954857 93.5804938154 0.6471508433 0.5267108208 -137.8210879417 258.9424789131 -137.8210879417 258.9424789131
Avg. annual Household T.V 0.0103373744 0.0026241533 3.9393180197 0.0011725534 0.0047744179 0.0159003308 0.0047744179 0.0159003308
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted QTY of T.V Residuals Standard Residuals Percentile QTY of T.V
1 370.6819269421 -120.6819269421 -2.5401222608 2.7777777778 250
2 370.6819269421 29.3180730579 0.6170890033 8.3333333333 330
3 370.6819269421 -40.6819269421 -0.8562762533 13.8888888889 360
4 391.3566757059 -31.3566757059 -0.659997665 19.4444444444 380
5 391.3566757059 53.6433242941 1.129088718 25 400
6 381.019301324 -1.019301324 -0.0214543308 30.5555555556 400
7 391.3566757059 48.6433242941 1.0238483426 36.1111111111 410
8 391.3566757059 8.6433242941 0.1819253388 41.6666666667 440
9 391.3566757059 58.6433242941 1.2343290935 47.2222222222 440
10 453.3809219971 46.6190780029 0.9812418546 52.7777777778 440
11 453.3809219971 -13.3809219971 -0.281642651 58.3333333333 445
12 453.3809219971 46.6190780029 0.9812418546 63.8888888889 450
13 453.3809219971 16.6190780029 0.3497996018 69.4444444444 460
14 494.7304195246 25.2695804754 0.5318760274 75 470
15 494.7304195246 -14.7304195246 -0.3100469763 80.5555555556 480
16 494.7304195246 -54.7304195246 -1.1519699801 86.1111111111 500
17 463.718296379 -53.718296379 -1.1306667361 91.6666666667 500
18 463.718296379 -3.718296379 -0.0782629814 97.2222222222 520
QE = β0 + β1PE+ β3I,
QTY of T.V price easter electirc T.V Avg. annual Household T.V
250 900 30000
400 800 30000
330 800 30000
360 800 32000
445 700 32000
380 700 31000
440 675 32000
400 675 32000
450 630 32000
500 630 38000
440 630 38000
500 595 38000
470 595 38000
520 595 42000
480 595 42000
440 625 42000
410 625 39000
460 625 39000
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8985760704
R Square 0.8074389543
Adjusted R Square 0.7817641482
Standard Error 31.1509688813
Observations 18
ANOVA
df SS MS F Significance F
Regression 2 61034.53484412 30517.26742206 31.448687533 0.0000043079
Residual 15 14555.7429336578 970.3828622439
Total 17 75590.2777777778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 882.6347559588 176.2887634498 5.0067556133 0.0001563103 506.8841529588 1258.3853589587 506.8841529588 1258.3853589587
price easter electirc T.V -0.6688998386 0.13501688 -4.9541941609 0.0001730906 -0.9566815048 -0.3811181724 -0.9566815048 -0.3811181724
Avg. annual Household T.V -0.0000866438 0.0026857742 -0.0322602554 0.9746898563 -0.0058112358 0.0056379483 -0.0058112358 0.0056379483
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted QTY of T.V Residuals Standard Residuals Percentile QTY of T.V
1 278.0255883942 -28.0255883942 -0.9577717244 2.7777777778 250
2 344.9155722558 55.0844277442 1.8825048953 8.3333333333 330
3 344.9155722558 -14.9155722558 -0.5097382135 13.8888888889 360
4 344.7422847352 15.2577152648 0.5214309171 19.4444444444 380
5 411.6322685967 33.3677314033 1.1403389358 25 400
6 411.7189123571 -31.7189123571 -1.0839907072 30.5555555556 400
7 428.3547645621 11.6452354379 0.3979747747 36.1111111111 410
8 428.3547645621 -28.3547645621 -0.9690212875 41.6666666667 440
9 458.4552572999 -8.4552572999 -0.2889575858 47.2222222222 440
10 457.9353947378 42.0646052622 1.4375537438 52.7777777778 440
11 457.9353947378 -17.9353947378 -0.6129403495 58.3333333333 445
12 481.3468890894 18.6531109106 0.6374682291 63.8888888889 450
13 481.3468890894 -11.3468890894 -0.3877788176 69.4444444444 460
14 481.000314048 38.999685952 1.3328104281 75 470
15 481.000314048 -1.000314048 -0.0341856341 80.5555555556 480
16 460.9333188895 -20.9333188895 -0.7153941123 86.1111111111 500
17 461.1932501705 -51.1932501705 -1.7495242848 91.6666666667 500
18 461.1932501705 -1.1932501705 -0.0407792071 97.2222222222 520
QTY of T.V price generally excellent T.V Avg. annual Household T.V
250 1400 30000
400 1500 30000
330 1200 30000
360 1200 32000
445 1200 32000
380 1000 31000
440 1000 32000
400 900 32000
450 900 32000
500 950 38000
440 800 38000
500 800 38000
470 750 38000
520 750 42000
480 700 42000
440 700 42000
410 700 39000
460 750 39000
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.7209613674
R Square 0.5197852933
Adjusted R Square 0.4557566657
Standard Error 49.1931994449
Observations 18
ANOVA
df SS MS F Significance F
Regression 2 39290.7147034073 19645.3573517036 8.1180139737 0.0040809937
Residual 15 36299.5630743705 2419.9708716247
Total 17 75590.2777777778
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 270.0289095074 245.0510439892 1.1019292353 0.2878599338 -252.2850244202 792.342843435 -252.2850244202 792.342843435
price generally excellent T.V -0.0810232665 0.087535501 -0.9256046474 0.3693043419 -0.2676007694 0.1055542364 -0.2676007694 0.1055542364
Avg. annual Household T.V 0.0066060908 0.004816518 1.3715490552 0.1903727413 -0.0036600744 0.0168722559 -0.0036600744 0.0168722559
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted QTY of T.V Residuals Standard Residuals Percentile QTY of T.V
1 354.7790591373 -104.7790591373 -2.2675050151 2.7777777778 250
2 346.676732487 53.323267513 1.1539593646 8.3333333333 330
3 370.9837124378 -40.9837124378 -0.8869212441 13.8888888889 360
4 384.1958939534 -24.1958939534 -0.523619045 19.4444444444 380
5 384.1958939534 60.8041060466 1.3158508631 25 400
6 393.7944564962 -13.7944564962 -0.2985233838 30.5555555556 400
7 400.400547254 39.599452746 0.8569647259 36.1111111111 410
8 408.5028739043 -8.5028739043 -0.1840091845 41.6666666667 440
9 408.5028739043 41.4971260957 0.8980319379 47.2222222222 440
10 444.0882551259 55.9117448741 1.2099761436 52.7777777778 440
11 456.2417451014 -16.2417451014 -0.351484722 58.3333333333 445
12 456.2417451014 43.7582548986 0.9469646249 63.8888888889 450
13 460.2929084265 9.7070915735 0.2100694452 69.4444444444 460
14 486.7172714577 33.2827285423 0.720265619 75 470
15 490.7684347828 -10.7684347828 -0.2330377852 80.5555555556 480
16 490.7684347828 -50.7684347828 -1.0986706831 86.1111111111 500
17 470.9501625094 -60.9501625094 -1.3190116451 91.6666666667 500
18 466.8989991843 -6.8989991843 -0.1493000164 97.2222222222 520
detection of autocorrelation:
Predicted QTY of T.V Residuals square of residuals differences square of differences
260.9869876347 -28.3179138322 801.9042438079 83.4512471655 6964.1106534828
410.8982343596 55.1333333333 3039.6844444444 -70 4900
323.116792938 -14.8666666667 221.0177777778 30 900
333.1376067964 15.1333333333 229.0177777778 18.4512471655 340.4485219636
453.7883730474 33.5845804989 1127.9240472848 -65 4225
390.2570051704 -31.4154195011 986.9285824322 43.3628117914 1880.3334464549
425.4301036624 11.9473922902 142.7401825371 -40 1600
396.1696231885 -28.0526077098 786.9487993172 20.0530612245 402.1252644731
450.4624680014 -7.9995464853 63.9927439698 50 2500
495.1551498136 42.0004535147 1764.0380954438 -60 3600
451.2644291028 -17.9995464853 323.9836736751 36.7079365079 1347.4726026707
493.4921972906 18.7083900227 350.0038572406 -30 900
478.8619570537 -11.2916099773 127.50045588 50 2500
498.9035847705 38.7083900227 1498.3394581476 -40 1600
484.2733445336 -1.2916099773 1.6682563335 -20.0353741497 401.4162173169
448.0781146583 -21.326984127 454.8402519526 -30 900
433.0468938706 -51.326984127 2634.4592995717 50 2500
447.6771341076 -1.326984127 1.7608868733 1.326984127 1.7608868733
14556.7528344671 37462.6675932353
V= 2.5735593658

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