Eastern Electric Produces a 25-inch thin-walled television. The company wants to get a better graph on the sensitivity of the quantity 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 In this case the obtained regression output is given below, SUMMARY OUTPUT Regression Statistics Multiple R 0.9806 R Square 0.9616 Adjusted R Square 0.9534 Standard Error 14.3947 Observations 18 ANOVA df SS MS F Significance F Regression 3 72689.3823 24229.7941 116.9353 0.0000 Residual 14 2900.8955 207.2068 Total 17 75590.2778 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 786.8849 82.4564 9.5430 0.0000 610.0336 963.7363 price easter electric T.V -1.2065 0.0950 -12.6959 0.0000 -1.4103 -1.0027 price generally excellent T.V 0.2926 0.0390 7.4998 0.0000 0.2089 0.3763 Avg. annual Household T.V 0.0050 0.0014 3.5410 0.0033 0.0020 0.0080 a. From the above output we can see that the estimated values for β0 β1 β2 β3 are 786.8849, -1.2065, 0.2926 and 0.0050 respectively. b. To check which of the estimated values I found in part a. are significantly different from zero (one-tailed tests) at the 5% level of significance I need to look at the t-test and the relevant output. A p-value of less than 0.05 in t-test would indicate that variable is significant. Now from the output we can see that the p-values for the t-test for each independent variable is less than 0.05 thus each of the independent variables are significant. c. The value of R^2 is 0.9616. 1. Use the normal distribution of SAT critical reading scores for which the mean is 513 and the standard deviation is 120. Assume the variable x is normally distributed. a) What percent of the SAT verbal scores are less than 650? b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575? 2. Find the z-score that has 7.5% of the distributions area to its right? 3.In a survey of women in a certain country (ages 20-29) the mean height was 66.1 inches with a standard deviation of 2.71 inches. Answer the following questions about the specified normal distribution. a) What height represents the 90th percentile?  b) What height represents the first quartile? Sheet1Eastern 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 ...

1. Eastern Electric Produces a 25-inch thin-walled television. The
company wants to get a better graph on the sensitivity of the
quantity 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
In this case the obtained regression output is given below,
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9806

2. R Square
0.9616
Adjusted R Square
0.9534
Standard Error
14.3947
Observations
18

3. ANOVA
df
SS
MS
F
Significance F
Regression
3
72689.3823
24229.7941
116.9353
0.0000
Residual
14
2900.8955
207.2068
Total
17
75590.2778

4. Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
786.8849
82.4564
9.5430
0.0000
610.0336
963.7363
price easter electric T.V
-1.2065
0.0950
-12.6959
0.0000
-1.4103
-1.0027
price generally excellent T.V
0.2926
0.0390
7.4998
0.0000

5. 0.2089
0.3763
Avg. annual Household T.V
0.0050
0.0014
3.5410
0.0033
0.0020
0.0080
a. From the above output we can see that the estimated values
for β0 β1 β2 β3 are 786.8849, -1.2065, 0.2926 and 0.0050
respectively.
b. To check which of the estimated values I found in part a. are
significantly different from zero (one-tailed tests) at the 5%
level of significance I need to look at the t-test and the relevant
output. A p-value of less than 0.05 in t-test would indicate that
variable is significant.
Now from the output we can see that the p-values for the t-test
for each independent variable is less than 0.05 thus each of the
independent variables are significant.
c. The value of R^2 is 0.9616.
1. Use the normal distribution of SAT critical reading scores for
which the mean is 513 and the standard deviation is 120.
Assume the variable x is normally distributed.
a) What percent of the SAT verbal scores are less than 650?
b) If 1000 SAT verbal scores are randomly selected, about how
many would you expect to be greater than 575?
2. Find the z-score that has 7.5% of the distributions area to its
right?
3.In a survey of women in a certain country (ages 20-29) the

6. mean height was 66.1 inches with a standard deviation of 2.71
inches. Answer the following questions about the specified
normal distribution.
a) What height represents the 90th percentile?
b) What height represents the first quartile?
Sheet1Eastern 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^2Analysis of Full modelQE = β0 +
β1PE + β2PG + β3I,Q = QTY of T.Vprice easter electric
T.Vprice generally excellent T.VAvg. annual Household
T.V2509001400300004008001500300003308001200300003608
00120032000445700120032000380700100031000440675100032
00040067590032000450630900320005006309503800044063080
03800050059580038000470595750380005205957504200048059
57004200044062570042000410625700390004606257503900076
751219517200637000SUMMARY OUTPUTRegression
StatisticsMultiple R0.9806240008R
Square0.9616234309Adjusted R Square0.9533998804Standard
Error14.3946803604Observations18ANOVAdfSSMSFSignifican
ce
FRegression372689.382260281624229.7940867605116.9353102
0640.0000000004Residual142900.8955174962207.2068226783T
otal1775590.2777777778CoefficientsStandard Errort StatP-

7. valueLower 95%Upper 95%Lower 95.0%Upper
95.0%Intercept786.884949383482.45637012359.54304619770.0
000001662610.0336249557963.7362738112610.0336249557963
.7362738112price easter electirc T.V-
1.20650766250.0950314902-12.69587228130.0000000045-
1.410329937-1.002685388-1.410329937-1.002685388price
generally excellent
T.V0.29260480470.03901487177.49982742990.00000287960.20
892622760.37628338190.20892622760.3762833819Avg. annual
Household
T.V0.00501040690.00141497973.54097451330.0032588210.001
97557740.00804523650.00197557740.0080452365RESIDUAL
OUTPUTPROBABILITY OUTPUTObservationPredicted QTY
of T.VResidualsStandard ResidualsPercentileQTY of
T.V1260.9869876347-10.9869876347-
0.84107950992.77777777782502410.8982343596-
10.8982343596-
0.83428523988.33333333333303323.1167929386.8832070620.5
26925542713.88888888893604333.137606796426.86239320362
.056378805619.44444444443805453.7883730474-
8.7883730474-0.6727704391254006390.2570051704-
10.2570051704-
0.785197650930.55555555564007425.430103662414.56989633
761.115359521536.11111111114108396.16962318853.8303768
1150.293224272141.66666666674409450.4624680014-
0.4624680014-
0.035403003347.222222222244010495.15514981364.84485018
640.370884573252.777777777844011451.2644291028-
11.2644291028-
0.862318300958.333333333344512493.49219729066.50780270
940.498187464663.888888888945013478.8619570537-
8.8619570537-
0.678403466369.444444444446014498.903584770521.0964152
2951.61497975347547015484.2733445336-4.2733445336-
0.327134483680.555555555648016448.0781146583-
8.0781146583-

8. 0.618398504186.111111111150017433.0468938706-
23.0468938706-
1.764293439291.666666666750018447.677134107612.3228658
9240.943344103997.22222222225207675considerQE = β0 +
β1PE + β2PGQTY of T.Vprice easter electirc T.Vprice
generally excellent
T.V2509001400400800150033080012003608001200445700120
03807001000440675100040067590045063090050063095044063
08005005958004705957505205957504805957004406257004106
2570046062575076751219517200SUMMARY
OUTPUTRegression StatisticsMultiple R0.9629398217R
Square0.9272531001Adjusted R Square0.9175535135Standard
Error19.1467288208Observations18ANOVAdfSSMSFSignifican
ce
FRegression270091.319409737235045.659704868695.59717684
50.0000000029Residual155498.9583680405366.597224536Tota
l1775590.2777777778CoefficientsStandard Errort StatP-
valueLower 95%Upper 95%Lower 95.0%Upper
95.0%Intercept1047.853513477549.186144519821.3038351289
0943.01572857911152.6912983759943.01572857911152.69129
83759price easter electirc T.V-1.23639756110.125904151-
9.82014930480.0000000634-1.5047559053-0.9680392168-
1.5047559053-0.9680392168price generally excellent
T.V0.22625029150.04551688194.97068960620.0001676330.129
23335480.32326722820.12923335480.3232672282RESIDUAL
OUTPUTPROBABILITY OUTPUTObservationPredicted QTY
of T.VResidualsStandard ResidualsPercentileQTY of
T.V1251.8461166828-1.8461166828-
0.10264632182.77777777782502398.11090194251.8890980575
0.10503613838.33333333333303330.2358144804-
0.2358144804-
0.013111570513.88888888893604330.235814480429.76418551
961.654924737119.44444444443805453.8755705861-
8.8755705861-0.4934924663254006408.625512278-
28.625512278-
1.591613126830.55555555564007439.53545130440.464548695

9. 60.025829469736.11111111114108416.9104221504-
16.9104221504-
0.940239937541.66666666674409472.548312398-
22.548312398-
1.253713458547.222222222244010483.86082697516.13917302
50.897357552752.777777777844011449.9232832439-
9.9232832439-
0.551746558158.333333333344512493.19719788096.80280211
910.378244030963.888888888945013481.8846833039-
11.8846833039-
0.660802775269.444444444446014481.884683303938.1153166
9612.11925773757547015470.57216872699.42783127310.5241
98828980.555555555648016433.48024189526.51975810480.36
2506441286.111111111150017433.4802418952-23.4802418952-
1.305529866491.666666666750018444.792756472215.2072435
2780.845541144897.22222222225207675considerQE = β0 +
β1PEQTY of T.Vprice easter electirc
T.V2509004008003308003608004457003807004406754006754
50630500630440630500595470595520595480595440625410625
460625767512195SUMMARY OUTPUTRegression
StatisticsMultiple R0.8985686363R
Square0.8074255941Adjusted R Square0.7953896937Standard
Error30.1628422426Observations18ANOVAdfSSMSFSignifican
ce
FRegression161033.524943310661033.524943310667.08476884
90.0000004081Residual1614556.7528344671909.7970521542To
tal1775590.2777777778CoefficientsStandard Errort StatP-
valueLower 95%Upper 95%Lower 95.0%Upper
95.0%Intercept877.256689342455.504655152415.80510115650
759.5920775337994.9213011512759.5920775337994.92130115
12price easter electirc T.V-0.66548752830.0812508582-
8.19052921670.0000004081-0.8377316522-0.4932434045-
0.8377316522-0.4932434045RESIDUAL
OUTPUTPROBABILITY OUTPUTObservationPredicted QTY
of T.VResidualsStandard ResidualsPercentileQTY of
T.V1278.3179138322-28.3179138322-

10. 0.96772834682.77777777782502344.866666666755.133333333
31.88411087898.33333333333303344.8666666667-
14.8666666667-
0.508049245413.88888888893604344.866666666715.13333333
330.517162236419.44444444443805411.415419501133.584580
49891.147709918254006411.4154195011-31.4154195011-
1.07358162630.55555555564007428.052607709811.947392290
20.408286791836.11111111114108428.0526077098-
28.0526077098-
0.958661850741.66666666674409457.9995464853-
7.9995464853-
0.273374230247.222222222244010457.999546485342.0004535
1471.435311572952.777777777844011457.9995464853-
17.9995464853-
0.615111390858.333333333344512481.291609977318.7083900
2270.639335208663.888888888945013481.2916099773-
11.2916099773-
0.385876273269.444444444446014481.291609977338.7083900
2271.32280952987547015481.2916099773-1.2916099773-
0.044139112680.555555555648016461.326984127-
21.326984127-0.728822386.111111111150017461.326984127-
51.326984127-
1.754033781891.666666666750018461.326984127-
1.326984127-0.045347978897.22222222225207675considerQE
= β0 + β2PGQTY of T.Vprice generally excellent
T.V2501400400150033012003601200445120038010004401000
40090045090050095044080050080047075052075048070044070
0410700460750767517200SUMMARY OUTPUTRegression
StatisticsMultiple R0.6779097794R
Square0.459561669Adjusted R Square0.4257842733Standard
Error50.529622229Observations18ANOVAdfSSMSFSignificanc
e
FRegression134738.394216133934738.394216133913.60559805
330.001989796Residual1640851.88356164382553.2427226027T
otal1775590.2777777778CoefficientsStandard Errort StatP-
valueLower 95%Upper 95%Lower 95.0%Upper

11. 95.0%Intercept599.828767123348.505708450512.36614795010.
0000000013497.0012594186702.656274828497.0012594186702
.656274828price generally excellent T.V-
0.18150684930.0492078284-3.68857669750.001989796-
0.2858227849-0.0771909137-0.2858227849-
0.0771909137RESIDUAL OUTPUTPROBABILITY
OUTPUTObservationPredicted QTY of T.VResidualsStandard
ResidualsPercentileQTY of T.V1345.7191780822-
95.7191780822-
1.95261840592.77777777782502327.568493150772.431506849
31.47756276518.33333333333303382.0205479452-
52.0205479452-
1.061190468213.88888888893604382.0205479452-
22.0205479452-
0.44920702519.44444444443805382.020547945262.979452054
81.2847460638254006418.3219178082-38.3219178082-
0.781745973630.55555555564007418.321917808221.67808219
180.442220912736.11111111114108436.4726027397-
36.4726027397-
0.744020966841.66666666674409436.472602739713.52739726
030.275951438447.222222222244010427.39726027472.602739
7261.481055821352.777777777844011454.6232876712-
14.6232876712-
0.29830699858.333333333344512454.623287671245.37671232
880.925659888363.888888888945013463.6986301376.3013698
630.128544467569.444444444446014463.69863013756.301369
8631.14851687277547015472.77397260277.22602739730.1474
06970980.555555555648016472.7739726027-32.7739726027-
0.668570953386.111111111150017472.7739726027-
62.7739726027-
1.280554396491.666666666750018463.698630137-
3.698630137-0.075450013597.2222222222520QE = β0 +
β3I,QTY of T.VAvg. annual Household
T.V2503000040030000330300003603200044532000380310004
40320004003200045032000500380004403800050038000470380
005204200048042000440420004103900046039000SUMMARY

12. OUTPUTRegression StatisticsMultiple R0.7016817107R
Square0.4923572232Adjusted R Square0.4606295497Standard
Error48.9724785659Observations18ANOVAdfSSMSFSignifican
ce
FRegression137217.419267648637217.419267648615.51822646
010.0011725534Residual1638372.85851012922398.3036568831
Total1775590.2777777778CoefficientsStandard Errort StatP-
valueLower 95%Upper 95%Lower 95.0%Upper
95.0%Intercept60.560695485793.58049381540.64715084330.52
67108208-137.8210879417258.9424789131-
137.8210879417258.9424789131Avg. annual Household
T.V0.01033737440.00262415333.93931801970.00117255340.00
477441790.01590033080.00477441790.0159003308RESIDUAL
OUTPUTPROBABILITY OUTPUTObservationPredicted QTY
of T.VResidualsStandard ResidualsPercentileQTY of
T.V1370.6819269421-120.6819269421-
2.54012226082.77777777782502370.681926942129.318073057
90.61708900338.33333333333303370.6819269421-
40.6819269421-
0.856276253313.88888888893604391.3566757059-
31.3566757059-
0.65999766519.44444444443805391.356675705953.643324294
11.129088718254006381.019301324-1.019301324-
0.021454330830.55555555564007391.356675705948.64332429
411.023848342636.11111111114108391.35667570598.6433242
9410.181925338841.66666666674409391.356675705958.64332
429411.234329093547.222222222244010453.380921997146.61
907800290.981241854652.777777777844011453.3809219971-
13.3809219971-
0.28164265158.333333333344512453.380921997146.61907800
290.981241854663.888888888945013453.380921997116.61907
800290.349799601869.444444444446014494.730419524625.26
958047540.53187602747547015494.7304195246-
14.7304195246-
0.310046976380.555555555648016494.7304195246-
54.7304195246-

13. 1.151969980186.111111111150017463.718296379-
53.718296379-
1.130666736191.666666666750018463.718296379-
3.718296379-0.078262981497.2222222222520QE = β0 + β1PE+
β3I,QTY of T.Vprice easter electirc T.VAvg. annual Household
T.V2509003000040080030000330800300003608003200044570
03200038070031000440675320004006753200045063032000500
63038000440630380005005953800047059538000520595420004
8059542000440625420004106253900046062539000SUMMARY
OUTPUTRegression StatisticsMultiple R0.8985760704R
Square0.8074389543Adjusted R Square0.7817641482Standard
Error31.1509688813Observations18ANOVAdfSSMSFSignifican
ce
FRegression261034.5348441230517.2674220631.4486875330.0
000043079Residual1514555.7429336578970.3828622439Total1
775590.2777777778CoefficientsStandard Errort StatP-
valueLower 95%Upper 95%Lower 95.0%Upper
95.0%Intercept882.6347559588176.28876344985.00675561330.
0001563103506.88415295881258.3853589587506.88415295881
258.3853589587price easter electirc T.V-
0.66889983860.13501688-4.95419416090.0001730906-
0.9566815048-0.3811181724-0.9566815048-0.3811181724Avg.
annual Household T.V-0.00008664380.0026857742-
0.03226025540.9746898563-0.00581123580.0056379483-
0.00581123580.0056379483RESIDUAL
OUTPUTPROBABILITY OUTPUTObservationPredicted QTY
of T.VResidualsStandard ResidualsPercentileQTY of
T.V1278.0255883942-28.0255883942-
0.95777172442.77777777782502344.915572255855.084427744
21.88250489538.33333333333303344.9155722558-
14.9155722558-
0.509738213513.88888888893604344.742284735215.25771526
480.521430917119.44444444443805411.632268596733.367731
40331.1403389358254006411.7189123571-31.7189123571-
1.083990707230.55555555564007428.354764562111.64523543
790.397974774736.11111111114108428.3547645621-

14. 28.3547645621-
0.969021287541.66666666674409458.4552572999-
8.4552572999-
0.288957585847.222222222244010457.935394737842.0646052
6221.437553743852.777777777844011457.9353947378-
17.9353947378-
0.612940349558.333333333344512481.346889089418.6531109
1060.637468229163.888888888945013481.3468890894-
11.3468890894-
0.387778817669.444444444446014481.00031404838.99968595
21.33281042817547015481.000314048-1.000314048-
0.034185634180.555555555648016460.9333188895-
20.9333188895-
0.715394112386.111111111150017461.1932501705-
51.1932501705-
1.749524284891.666666666750018461.1932501705-
1.1932501705-0.040779207197.2222222222520QTY of
T.Vprice generally excellent T.VAvg. annual Household
T.V2501400300004001500300003301200300003601200320004
45120032000380100031000440100032000400900320004509003
20005009503800044080038000500800380004707503800052075
04200048070042000440700420004107003900046075039000SU
MMARY OUTPUTRegression StatisticsMultiple
R0.7209613674R Square0.5197852933Adjusted R
Square0.4557566657Standard
Error49.1931994449Observations18ANOVAdfSSMSFSignifican
ce
FRegression239290.714703407319645.35735170368.118013973
70.0040809937Residual1536299.56307437052419.9708716247T
otal1775590.2777777778CoefficientsStandard Errort StatP-
valueLower 95%Upper 95%Lower 95.0%Upper
95.0%Intercept270.0289095074245.05104398921.10192923530.
2878599338-252.2850244202792.342843435-
252.2850244202792.342843435price generally excellent T.V-
0.08102326650.087535501-0.92560464740.3693043419-
0.26760076940.1055542364-0.26760076940.1055542364Avg.

15. annual Household
T.V0.00660609080.0048165181.37154905520.1903727413-
0.00366007440.0168722559-
0.00366007440.0168722559RESIDUAL
OUTPUTPROBABILITY OUTPUTObservationPredicted QTY
of T.VResidualsStandard ResidualsPercentileQTY of
T.V1354.7790591373-104.7790591373-
2.26750501512.77777777782502346.67673248753.3232675131.
15395936468.33333333333303370.9837124378-40.9837124378-
0.886921244113.88888888893604384.1958939534-
24.1958939534-
0.52361904519.44444444443805384.195893953460.804106046
61.3158508631254006393.7944564962-13.7944564962-
0.298523383830.55555555564007400.40054725439.599452746
0.856964725936.11111111114108408.5028739043-
8.5028739043-
0.184009184541.66666666674409408.502873904341.49712609
570.898031937947.222222222244010444.088255125955.91174
487411.209976143652.777777777844011456.2417451014-
16.2417451014-
0.35148472258.333333333344512456.241745101443.75825489
860.946964624963.888888888945013460.29290842659.707091
57350.210069445269.444444444446014486.717271457733.282
72854230.7202656197547015490.7684347828-10.7684347828-
0.233037785280.555555555648016490.7684347828-
50.7684347828-
1.098670683186.111111111150017470.9501625094-
60.9501625094-
1.319011645191.666666666750018466.8989991843-
6.8989991843-0.149300016497.2222222222520detection of
autocorrelation:Predicted QTY of T.VResidualssquare of
residualsdifferencessquare of differences260.9869876347-
28.3179138322801.904243807983.45124716556964.110653482
8410.898234359655.13333333333039.6844444444-
704900323.116792938-
14.8666666667221.017777777830900333.137606796415.13333

16. 33333229.017777777818.4512471655340.4485219636453.7883
73047433.58458049891127.9240472848-
654225390.2570051704-
31.4154195011986.928582432243.36281179141880.333446454
9425.430103662411.9473922902142.7401825371-
401600396.1696231885-
28.0526077098786.948799317220.0530612245402.1252644731
450.4624680014-
7.999546485363.9927439698502500495.155149813642.000453
51471764.0380954438-603600451.2644291028-
17.9995464853323.983673675136.70793650791347.472602670
7493.492197290618.7083900227350.0038572406-
30900478.8619570537-
11.2916099773127.50045588502500498.903584770538.708390
02271498.3394581476-401600484.2733445336-
1.29160997731.6682563335-
20.0353741497401.4162173169448.0781146583-
21.326984127454.8402519526-30900433.0468938706-
51.3269841272634.4592995717502500447.6771341076-
1.3269841271.76088687331.3269841271.760886873314556.752
834467137462.6675932353V=2.5735593658
Sheet1