Firm Chair

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Firm Chair Case AnalysisGroup-6Durga Prasad M105/13Sourav Mukhobadhya M149/13Vivek Prasad M079/13Introduction:Firm produces chairs of various typesDifferent price points observedTotal price, order quantity and order numbers givenRequired: an appropriate price model through regression analysisBoth single and multiple regression analysis doneAnalysis of anova of regression and statistics

Methodology-1:To get a general idea, a scatter plot is developed of total price~total quantity.In order to graphically visualize the price point breaks and fall in the marginal price per chair at certain order points, a scatter plot of the unit price~quantity is also developedPricing ClustersQuantityPer unit PricePricing Cluster formed between0 to 200200 to 400400 to 600Methodology-2:Therafter, having observed the distinct Price points and clustering of the prices at quantities of 0-200,200-400 and 400+, appropriate regression models are developed by adding and removing variables.First, a simple regression model is developed with price as the dependent variable and quantity as the independent variable.The results are decent with an R2 of 96% and a significant X variable.QuantityTotal PriceRegression: Total Price Vs. QuantityRegression StatisticsMultiple R0.98370116R Square0.967667972Adjusted R Square0.967258706Standard Error2114.867321Observations81CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept7779.936292594.872208313.078332091.84701E-216595.872788963.9998046595.872788963.999804Quantity100.34662752.06368080648.625071881.22804E-6096.23897363104.454281496.23897363104.4542814Methodology-3However, given the pricing structure, a better R2 can be achieved through introduction of appropriate variables that better proxy the price structure.Thus, 2 categorical variables are introduced to represent the price points-X1 and X2.For the quantity range 0-200,we code X1=1 and X2=0;For the range 200-400, we code X1=0 and X2=1;For 400 and beyond, X1=X2=0;This helps build the 3 different ranges into the model and helps the regression analysis identify the 3 ranges.

The equation:Price=-5614.22+124.37(Qty) + 9578.04(X1) + 7352.62(X2)Methodology-4:However, to take the model forward, we now introduce two interaction terms to check if there is any interaction between the variables-Qty and X1/X2.Two interaction variables,Int1 and int2 are introduced; int1=Qty*X1, and int2=Qty*X2.A regression is run again to check for adequacy.

The Equation: price=7269.24+96.9(Qty)-8384.23(X1)-5977.68(X2)+61.48(Int1)+29.034(Int2)While the R2 value increases on introducing interaction variables , from 0.9828 to 0.9867, and thus explains variation better;And the regression is also significant, thus rejection the null hypothesis;But on analyzing the individual variable statistics, it is seen that X2 is insignificant at the 95% CI,with p=0.126, >>0.05This may be overlooked if we reduce the CI to 90%, and p=0.126 will be nearly equal to 0.1Thank Youfinal prepared data OrderTotal Priceunit priceQuantityX1X2int1int2481323014790109006114518161.311111111190109004117163143.0251201012001119238147.98461538461301013001419952153.47692307691301013003219164147.41538461541301013004219117147.05384615381301013004418408141.61301013005917672135.93846153851301013006219008146.21538461541301013008122735162.39285714291401014002322455149.71501015002522916152.77333333331501015004023680157.86666666671501015007121321142.14150101500622715141.968751601016002123625147.656251601016002624881155.506251601016002824246151.53751601016003524904155.651601016006926369164.806251601016005426183154.01764705881701017002426590147.72222222221801018003427987155.48333333331801018003627318151.76666666671801018004728295157.19444444441801018001927907146.87894736841901019004529253153.96315789471901019003129647148.2352000102001826770127.47619047622100102102025924123.44761904762100102102927874126.72200102204630552138.8727272727220010220728768125.0782608696230010230930085130.80434782612300102301630846134.11304347832300102307330061130.72300102305531980133.252400102407431763132.34583333332400102407631199129.9958333333240010240529306117.2242500102503033024132.0962500102505332896131.5842500102501233981130.6961538462260010260135746132.3925925926270010270834435127.5370370372700102701035890132.92592592592700102704934706128.54074074072700102707237110137.4444444444270010270335518126.852800102803836304129.65714285712800102806737764134.87142857142800102806839587131.95666666673000103007939035130.1166666667300010300239495127.4032258065310010310443012138.74838709683100103106641815134.88709677423100103102240712127.2253200103204342115131.6093753200103207742731133.5343753200103201542478128.72121212123300103306444112129.74117647063400103401344688127.683500103502746604129.45555555563600103607545239125.66388888893600103607846379128.83055555563600103605747496128.36756756763700103703951396131.78461538463900103906049889127.92051282053900103905851804129.5140000003745428110.841000005147204112.390476190542000003346810106.386363636444000005650069113.793181818244000008047790108.613636363644000005253185110.802083333348000007053732111.941666666748000005056097112.19450000006360239113.65849056653000001760176111.43703703754000006560294109.62545454555500000

final prepared data (2)OrderTotal Priceunit priceQuantityX1int1int248132301479019006114518161.31111111119019004117163143.025120112001119238147.9846153846130113001419952153.4769230769130113003219164147.4153846154130113004219117147.0538461538130113004418408141.6130113005917672135.9384615385130113006219008146.2153846154130113008122735162.3928571429140114002322455149.7150115002522916152.7733333333150115004023680157.8666666667150115007121321142.1415011500622715141.96875160116002123625147.65625160116002624881155.50625160116002824246151.5375160116003524904155.65160116006926369164.80625160116005426183154.0176470588170117002426590147.7222222222180118003427987155.4833333333180118003627318151.7666666667180118004728295157.1944444444180118001927907146.8789473684190119004529253153.9631578947190119003129647148.235200002001826770127.4761904762210002102025924123.4476190476210002102927874126.7220002204630552138.872727272722000220728768125.078260869623000230930085130.8043478261230002301630846134.1130434783230002307330061130.7230002305531980133.25240002407431763132.3458333333240002407631199129.995833333324000240529306117.224250002503033024132.096250002505332896131.584250002501233981130.696153846226000260135746132.392592592627000270834435127.537037037270002701035890132.9259259259270002704934706128.5407407407270002707237110137.444444444427000270335518126.85280002803836304129.6571428571280002806737764134.8714285714280002806839587131.9566666667300003007939035130.116666666730000300239495127.403225806531000310443012138.7483870968310003106641815134.8870967742310003102240712127.225320003204342115131.609375320003207742731133.534375320003201542478128.7212121212330003306444112129.7411764706340003401344688127.68350003502746604129.4555555556360003607545239125.6638888889360003607846379128.8305555556360003605747496128.3675675676370003703951396131.7846153846390003906049889127.9205128205390003905851804129.514000003745428110.84100005147204112.39047619054200003346810106.38636363644400005650069113.79318181824400008047790108.61363636364400005253185110.80208333334800007053732111.94166666674800005056097112.1945000006360239113.6584905665300001760176111.4370370375400006560294109.6254545455550000

2 variable regressionSUMMARY OUTPUT

Regression StatisticsMultiple R0.9837011599R Square0.967667972Adjusted R Square0.9672587059Standard Error2114.8673213133Observations81ANOVAdfSSMSFSignificance FRegression110575155592.278110575155592.27812364.39761548490Residual79353340439.1539474472663.78675883Total8010928496031.4321

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept7779.9362921428594.872208289313.078332091706595.87278009328963.99980419236595.87278009328963.9998041923Quantity100.34662752152.063680805848.6250718815096.2389736278104.454281415296.2389736278104.4542814152

without interactionSUMMARY OUTPUT

Regression StatisticsMultiple R0.9917165875R Square0.98350179Adjusted R Square0.9828590026Standard Error1530.217804068Observations81

ANOVAdfSSMSFSignificance FRegression310748195408.78483582731802.928271530.05766022870Residual77180300622.6472772341566.52788671Total8010928496031.4321

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept-5614.22862970891845.9164397524-3.04143162110.0032180791-9289.9178538856-1938.5394055322-9289.9178538856-1938.5394055322Quantity124.3692262093.820140556832.55619115560116.7623545342131.9760978837116.7623545342131.9760978837X19578.03700279821331.17165225587.19519303660.00000000046927.335599227412228.73840636916927.335599227412228.7384063691X27352.6239206254867.83138028998.472410755805624.55087016739080.69697108365624.55087016739080.6969710836

with 2 interactionsSUMMARY OUTPUT

Regression StatisticsMultiple R0.9937632751R Square0.987565447Adjusted R Square0.98673647671.4395314709Standard Error1346.0607397855-0.7063025628Observations81


CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept7269.24249228183685.54586330081.9723652240.0522546361-72.741360673814611.2263452374-72.741360673814611.2263452374Quantity96.90889699697.811732610812.4055573616081.3471276364112.470666357481.3471276364112.4706663574X1-8384.23260635043974.6020590643-2.10945208650.0382425846-16302.0459295142-466.4192831866-16302.0459295142-466.4192831866X2-5977.68666566453864.1480670737-1.54696107960.1260821291-13675.46435346571720.0910221366-13675.46435346571720.0910221366int161.480988934612.54882570234.89934200960.000005436.482446222886.479531646536.482446222886.4795316465int229.03424828738.78659125013.30438135350.001461328811.530460931846.538035642911.530460931846.5380356429

removing insignificant variableSUMMARY OUTPUT


CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 90.0%Upper 90.0%Intercept1831.36689681971117.63613074351.63860745590.1054287069-394.59837233144057.3321659707-29.66641890193692.4002125412Quantity108.37055683832.498009236743.38276866550103.3953402631113.3457734136104.2109933771112.5301202996X1-2946.35701088821871.8735311101-1.57401499720.119637965-6674.5162515192781.8022297427-6063.3097546187170.5957328422int150.019329093210.22046217634.8940378850.000005408229.663514518770.375143667733.000712667967.0379455186int215.73350840811.82730264428.6102367653012.094119782219.37289703412.690772937118.7762438791RESIDUAL OUTPUT

ObservationPredicted Total PriceResiduals113140.099619771889.9003802282213140.09961977181377.9003802282317891.7961977186-728.7961977186419475.6950570342-237.6950570342519475.6950570342476.3049429658619475.6950570342-311.6950570342719475.6950570342-358.6950570342819475.6950570342-1067.6950570342919475.6950570342-1803.69505703421019475.6950570342-467.69505703421121059.59391634981675.40608365021222643.4927756654-188.49277566541322643.4927756654272.50722433461422643.49277566541036.50722433461522643.4927756654-1322.49277566541624227.391634981-1512.3916349811724227.391634981-602.3916349811824227.391634981653.6083650191924227.39163498118.6083650192024227.391634981676.6083650192124227.3916349812141.6083650192225811.2904942966371.70950570342327395.1893536122-805.18935361222427395.1893536122591.81064638782527395.1893536122-77.18935361222627395.1893536122899.81064638782728979.0882129278-1072.08821292782828979.0882129278273.91178707222926652.17994610962994.82005389043027893.2205985741-1123.2205985743127893.2205985741-1969.2205985743229134.2612510385-1260.26125103853329134.26125103851417.73874896153430375.301903503-1607.3019035033530375.301903503-290.3019035033630375.301903503470.6980964973730375.301903503-314.3019035033831616.3425559675363.65744403253931616.3425559675146.65744403254031616.3425559675-417.34255596754132857.383208432-3551.3832084324232857.383208432166.6167915684332857.38320843238.6167915684434098.4238608965-117.42386089654535339.464513361406.5354866394635339.464513361-904.4645133614735339.464513361550.5354866394835339.464513361-633.4645133614935339.4645133611770.5354866395036580.5051658255-1062.50516582555136580.5051658255-276.50516582555236580.50516582551183.49483417455339062.5864707545524.41352924555439062.5864707545-27.58647075455540303.627123219-808.6271232195640303.6271232192708.3728767815740303.6271232191511.3728767815841544.6677756835-832.66777568355941544.6677756835570.33222431656041544.66777568351186.33222431656142785.708428148-307.7084281486244026.749080612585.25091938756345267.789733077-579.7897330776446508.830385541595.16961445856546508.8303855415-1269.83038554156646508.8303855415-129.83038554156747749.871038006-253.8710380066850231.9523429351164.0476570656950231.952342935-342.9523429357045179.5896321586624.4103678427146263.2952005414-835.29520054147247347.0007689249-143.00076892497349514.4119056918-2704.41190569187449514.4119056918554.58809430827549514.4119056918-1724.41190569187653849.2341792256-664.23417922567753849.2341792256-117.23417922567856016.645315992580.35468400757959267.7620211429971.23797885718060351.4675895264-175.46758952648161435.1731579098-1141.1731579098

final prepared data OrderTotal Priceunit priceQuantityX1X2int1int2481323014790109006114518161.311111111190109004117163143.0251201012001119238147.98461538461301013001419952153.47692307691301013003219164147.41538461541301013004219117147.05384615381301013004418408141.61301013005917672135.93846153851301013006219008146.21538461541301013008122735162.39285714291401014002322455149.71501015002522916152.77333333331501015004023680157.86666666671501015007121321142.14150101500622715141.968751601016002123625147.656251601016002624881155.506251601016002824246151.53751601016003524904155.651601016006926369164.806251601016005426183154.01764705881701017002426590147.72222222221801018003427987155.48333333331801018003627318151.76666666671801018004728295157.19444444441801018001927907146.87894736841901019004529253153.96315789471901019003129647148.2352000102001826770127.47619047622100102102025924123.44761904762100102102927874126.72200102204630552138.8727272727220010220728768125.0782608696230010230930085130.80434782612300102301630846134.11304347832300102307330061130.72300102305531980133.252400102407431763132.34583333332400102407631199129.9958333333240010240529306117.2242500102503033024132.0962500102505332896131.5842500102501233981130.6961538462260010260135746132.3925925926270010270834435127.5370370372700102701035890132.92592592592700102704934706128.54074074072700102707237110137.4444444444270010270335518126.852800102803836304129.65714285712800102806737764134.87142857142800102806839587131.95666666673000103007939035130.1166666667300010300239495127.4032258065310010310443012138.74838709683100103106641815134.88709677423100103102240712127.2253200103204342115131.6093753200103207742731133.5343753200103201542478128.72121212123300103306444112129.74117647063400103401344688127.683500103502746604129.45555555563600103607545239125.66388888893600103607846379128.83055555563600103605747496128.36756756763700103703951396131.78461538463900103906049889127.92051282053900103905851804129.5140000003745428110.841000005147204112.390476190542000003346810106.386363636444000005650069113.793181818244000008047790108.613636363644000005253185110.802083333348000007053732111.941666666748000005056097112.19450000006360239113.65849056653000001760176111.43703703754000006560294109.62545454555500000

final prepared data (2)OrderTotal Priceunit priceQuantityX1int1int248132301479019006114518161.31111111119019004117163143.025120112001119238147.9846153846130113001419952153.4769230769130113003219164147.4153846154130113004219117147.0538461538130113004418408141.6130113005917672135.9384615385130113006219008146.2153846154130113008122735162.3928571429140114002322455149.7150115002522916152.7733333333150115004023680157.8666666667150115007121321142.1415011500622715141.96875160116002123625147.65625160116002624881155.50625160116002824246151.5375160116003524904155.65160116006926369164.80625160116005426183154.0176470588170117002426590147.7222222222180118003427987155.4833333333180118003627318151.7666666667180118004728295157.1944444444180118001927907146.8789473684190119004529253153.9631578947190119003129647148.235200002001826770127.4761904762210002102025924123.4476190476210002102927874126.7220002204630552138.872727272722000220728768125.078260869623000230930085130.8043478261230002301630846134.1130434783230002307330061130.7230002305531980133.25240002407431763132.3458333333240002407631199129.995833333324000240529306117.224250002503033024132.096250002505332896131.584250002501233981130.696153846226000260135746132.392592592627000270834435127.537037037270002701035890132.9259259259270002704934706128.5407407407270002707237110137.444444444427000270335518126.85280002803836304129.6571428571280002806737764134.8714285714280002806839587131.9566666667300003007939035130.116666666730000300239495127.403225806531000310443012138.7483870968310003106641815134.8870967742310003102240712127.225320003204342115131.609375320003207742731133.534375320003201542478128.7212121212330003306444112129.7411764706340003401344688127.68350003502746604129.4555555556360003607545239125.6638888889360003607846379128.8305555556360003605747496128.3675675676370003703951396131.7846153846390003906049889127.9205128205390003905851804129.514000003745428110.84100005147204112.39047619054200003346810106.38636363644400005650069113.79318181824400008047790108.61363636364400005253185110.80208333334800007053732111.94166666674800005056097112.1945000006360239113.6584905665300001760176111.4370370375400006560294109.6254545455550000

2 variable regressionSUMMARY OUTPUT


CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept7779.9362921428594.872208289313.078332091706595.87278009328963.99980419236595.87278009328963.9998041923Quantity100.34662752152.063680805848.6250718815096.2389736278104.454281415296.2389736278104.4542814152

without interactionSUMMARY OUTPUT

Regression StatisticsMultiple R0.9917165875R Square0.98350179Adjusted R Square0.9828590026Standard Error1530.217804068Observations81


CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept-5614.22862970891845.9164397524-3.04143162110.0032180791-9289.9178538856-1938.5394055322-9289.9178538856-1938.5394055322Quantity124.3692262093.820140556832.55619115560116.7623545342131.9760978837116.7623545342131.9760978837X19578.03700279821331.17165225587.19519303660.00000000046927.335599227412228.73840636916927.335599227412228.7384063691X27352.6239206254867.83138028998.472410755805624.55087016739080.69697108365624.55087016739080.6969710836

with 2 interactionsSUMMARY OUTPUT

Regression StatisticsMultiple R0.9937632751R Square0.987565447Adjusted R Square0.98673647671.4395314709Standard Error1346.0607397855-0.7063025628Observations81


CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept7269.24249228183685.54586330081.9723652240.0522546361-72.741360673814611.2263452374-72.741360673814611.2263452374Quantity96.90889699697.811732610812.4055573616081.3471276364112.470666357481.3471276364112.4706663574X1-8384.23260635043974.6020590643-2.10945208650.0382425846-16302.0459295142-466.4192831866-16302.0459295142-466.4192831866X2-5977.68666566453864.1480670737-1.54696107960.1260821291-13675.46435346571720.0910221366-13675.46435346571720.0910221366int161.480988934612.54882570234.89934200960.000005436.482446222886.479531646536.482446222886.4795316465int229.03424828738.78659125013.30438135350.001461328811.530460931846.538035642911.530460931846.5380356429

removing insignificant variableSUMMARY OUTPUT


CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 90.0%Upper 90.0%Intercept1831.36689681971117.63613074351.63860745590.1054287069-394.59837233144057.3321659707-29.66641890193692.4002125412Quantity108.37055683832.498009236743.38276866550103.3953402631113.3457734136104.2109933771112.5301202996X1-2946.35701088821871.8735311101-1.57401499720.119637965-6674.5162515192781.8022297427-6063.3097546187170.5957328422int150.019329093210.22046217634.8940378850.000005408229.663514518770.375143667733.000712667967.0379455186int215.73350840811.82730264428.6102367653012.094119782219.37289703412.690772937118.7762438791RESIDUAL OUTPUT

ObservationPredicted Total PriceResiduals113140.099619771889.9003802282213140.09961977181377.9003802282317891.7961977186-728.7961977186419475.6950570342-237.6950570342519475.6950570342476.3049429658619475.6950570342-311.6950570342719475.6950570342-358.6950570342819475.6950570342-1067.6950570342919475.6950570342-1803.69505703421019475.6950570342-467.69505703421121059.59391634981675.40608365021222643.4927756654-188.49277566541322643.4927756654272.50722433461422643.49277566541036.50722433461522643.4927756654-1322.49277566541624227.391634981-1512.3916349811724227.391634981-602.3916349811824227.391634981653.6083650191924227.39163498118.6083650192024227.391634981676.6083650192124227.3916349812141.6083650192225811.2904942966371.70950570342327395.1893536122-805.18935361222427395.1893536122591.81064638782527395.1893536122-77.18935361222627395.1893536122899.81064638782728979.0882129278-1072.08821292782828979.0882129278273.91178707222926652.17994610962994.82005389043027893.2205985741-1123.2205985743127893.2205985741-1969.2205985743229134.2612510385-1260.26125103853329134.26125103851417.73874896153430375.301903503-1607.3019035033530375.301903503-290.3019035033630375.301903503470.6980964973730375.301903503-314.3019035033831616.3425559675363.65744403253931616.3425559675146.65744403254031616.3425559675-417.34255596754132857.383208432-3551.3832084324232857.383208432166.6167915684332857.38320843238.6167915684434098.4238608965-117.42386089654535339.464513361406.5354866394635339.464513361-904.4645133614735339.464513361550.5354866394835339.464513361-633.4645133614935339.4645133611770.5354866395036580.5051658255-1062.50516582555136580.5051658255-276.50516582555236580.50516582551183.49483417455339062.5864707545524.41352924555439062.5864707545-27.58647075455540303.627123219-808.6271232195640303.6271232192708.3728767815740303.6271232191511.3728767815841544.6677756835-832.66777568355941544.6677756835570.33222431656041544.66777568351186.33222431656142785.708428148-307.7084281486244026.749080612585.25091938756345267.789733077-579.7897330776446508.830385541595.16961445856546508.8303855415-1269.83038554156646508.8303855415-129.83038554156747749.871038006-253.8710380066850231.9523429351164.0476570656950231.952342935-342.9523429357045179.5896321586624.4103678427146263.2952005414-835.29520054147247347.0007689249-143.00076892497349514.4119056918-2704.41190569187449514.4119056918554.58809430827549514.4119056918-1724.41190569187653849.2341792256-664.23417922567753849.2341792256-117.23417922567856016.645315992580.35468400757959267.7620211429971.23797885718060351.4675895264-175.46758952648161435.1731579098-1141.1731579098

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