ABC AUCTIONS ANALYSIS1
Predicting Profit for ABC Auctions
BSAD 6312: Regression
Demetria Henderson
College of Business
University of Texas at Arlington
ABC Auctions is an established wholesale vehicle auction that has been in business for over 50 years. The company has over 20,000 employees in 100 locations worldwide. Within North America, the company operates over 75 auctions and handles approximately 500,000 cars with 11,000 full time employees. The company does business with more than 75,000 auto dealers and generates annual revenues of a billion dollars.
In an effort to understand the performance of the company, archival data was collected from seventy-five of the North American auction locations. The variables included such items as total number of cars sold, gross revenue, and earnings (see Appendix A for a full list of variables). The purpose of this study is to determine which variables predict the profitability of ABC Auctions by using multiple regression analysis.
The dependent variable of profitability was defined as earnings as a percentage of revenue. A total of seven independent variables: legacy; full-time turnover rate; part-time turnover rate; cars sold; workman’s comp claims per 10,000 cars consigned; lot damage per cars consigned; and Occupational and Safety Health Administration (OSHA) incidents per 10,000 cars consigned, were selected to run through the All Possible Regressions Procedure in NCSS. The All Possible Regressions Report (see Appendix B) was utilized to help determine which variables generated the best model, that is, which model did a better job of explaining the relationship with auction performance and the independent variables. In reviewing the results of the R2 vs. Variable Count Plot, it was determined that four variables would be sufficient in the model, as there was not much increase in variance explained beyond four variables.The model chosen for the initial run included number of cars sold, full-time turnover, lot damage per car, and OHSA per car. In the model chosen, the R2 was .5735 which indicates that the total variance explained by the model was 57.3% which was larger than the next best model which accounted for only 53.6% of the variance based on the R2 statistic.
In reviewing the results of the model (see Appendix B), all independent variables except for number of cars sold were statistically significant from zero at an α=.05 level. There appeared to be an issue with the variable for number of cars sold, as it had a p-value = 1.0; and NCSS was not able to compute confidence intervals for this independent variable. Additionally, there was no issue with multicollinearity and normality was not violated based on the results of the statistical tests. Additionally, the normal probability plot had all points falling within the bands and the histogram of the residuals followed a nice bell shape curve, further suggesting that the assumption of normality was not being violated. The residual plots seemed to have good random scatter about the mean suggesting that there was no clear evidence of a violation with independence or equal variance. Observations 41 and 68, auctions located in Lexington and St. John’s respectively, based on the values of Rstudent. In addition to the results of the t-test of the parameter, the partial residual plot for number of cars sold did not yield a linear relationship, suggesting that a transformation may be necessary. In addition, the linear relationship in the partial residual plot for OSHA accidents was not very strong.
Therefore, several transformations were attempted in an effort to improve the model and the relationship of number of cars sold with firm performance. The first transformation attempted took the natural log of the number of cars sold. The R2 for the model increased to .5902, and all independent variables in the model were significantly different from zero; however, the b0 was no longer significant. The assumptions for normality, independence, and equal variance did not appear to be violated. The same auctions from the original run presented as outliers in addition to Lincoln. The partial residual plot for number of cars sold appeared to be more linear. Next, I tried the log of the number of cars sold and saw very similar results to the model which used the natural log. However, the intercept was still not significant, so I then attempted an interaction term with the natural log of number of cars sold with the rate of the full-time employee turnover. This model had an R2 of .5903, unfortunately the interaction term and the variables which were included in the interaction term were not significantly different from zero. Lastly, I tried the inverse of the number of cars sold.
The model with the inverse of number of cars sold resulted in the best results for the data (see Appendix D). The final model is:
EarningsPercent = 51.2 – .13*ftturn – 82079.59*inverse_sold – 11.47*lotdampercar – 1.11*oshapercar
The model had an R2 of .5968 indicating that 59.7% of the total variance could be explained by the model. The result of the F-test for the model was significant with a p-value less than .05. In addition, all parameter estimates were found to be significantly different from zero with p-values less than .05. The five statistical tests for normality all failed to reject the null hypothesis, suggesting that normality was not violated. Furthermore, the plot of the histogram of the residuals along with the normal probability affirmed that normality did not appear to be violated. Multicollinearity was not introduced into the model as there were not variance inflation factors (VIF) greater than 10. The residual plots all show random scatter about the mean of zero indicating no evidence of violation with the assumptions for independence or equal variance. In addition the partial residual plots for the independent variables all show a negative linear pattern. Three auction locations presented as outliers with an Rstudent greater than 2: Lexington, Lincoln, and St. John’s. Interestingly, both Lexington and Lincoln have fairly high profits, however, based on the model, their predicted profits are estimated to be much lower as the number of damages and accidents reported are very high in comparison to auction lots within the similar range of profit margins. Whereas, St. John’s appears to be underperforming based on the model in large part due to its low safety numbers. The Central Arkansas and Ocala auction locations, very poor performers,have a little leverage with Hat’s Matrix values of .2 and .3.
In conclusion, the model indicates that performance, employee turnover, and safety are all important in determining the profits for the ABC Auction locations. It is clear that as full-time employee turnover, number of accidents reported, and the amount of damages increases; the earnings profits are negatively impacted. Although, the parameter estimate for the inverse function of the number of cars sold is negative, as the number of cars increases, the inverse function gets smaller, thus resulting in a less negative impact on profit earnings.
Appendix A
Archival Performance Auction Data
Variable Name / DefinitionIdno / Numerical identifier for cases
Auction / Name of auction unit
Consign / Total number of cars consigned
Sold / Total number of cars sold
Lotdamag / Total lot damage per year
Grossrev / Gross revenue per year
Ebitdal / Earnings
Ftterm / Full time terminations per year
Fthead / Full time headcount at end of year
Ptterm / Part time terminations per year
Pthead / Part time headcount at end of year
Wcclaims / Workman’s comp claims per year
OSHA / OSHA reportable incidents per year
Legacy / Auction origin within ABC
Earningspercent / Earnings/Revenue*100 (calculated)
Ftturn / Full time turnover percentage (calculated) (Terminations/Headcount*100)
Ptturn / Part time turnover percentage (calculated)
Wcpercar / Workman’s Comp claims per 10,000 cars consigned (calc) (Comp claims/Consignments*10000)
Lotdampercar / Lot damage per cars consigned (calculated)
(Lot damage/Consignments)
OSHApercar / OSHA incidents per 10,000 cars consigned (calculated) (OSHA/Consignments*10000)
Appendix B
All Possible Regressions Report
All Possible Results Section
ModelRoot
SizeR-SquaredMSECpModel
10.02218711.91887 85.785165A (sold)
10.0000000 -71.000000E (wcpercar)
10.0000000 -71.000000G (lotdampercar)
10.0000000 -71.000000B (legacy)
10.0000000 -71.000000F (oshapercar)
10.0000000 -71.000000C (ftturn)
10.0000000 -71.000000D (ptturn)
20.4554258.956353 18.318634AG
20.19163110.91207 60.615954AF
20.13207311.30691 70.165727AC
20.11503511.41735 72.897641AE
20.05541511.79567 82.457178AD
20.03454211.92529 85.804049AB
30.5213738.45547 9.744251ACG
30.4890448.736374 14.928088AFG
30.4664028.927839 18.558477ADG
30.4559759.014648 20.230416ABG
30.4558669.015551 20.247887AEG
30.3346219.969513 39.688651ACF
30.29105310.29073 46.674398ACE
30.22098710.78728 57.909056ADF
30.19321610.97786 62.361795ABF
30.19263410.98182 62.455113AEF
40.5734528.039024 3.393803ACFG
40.5340538.402098 9.711158ACEG
40.5248578.484607 11.185708ACDG
40.5214448.515019 11.732858ABCG
40.5035448.672813 14.603107AEFG
40.5007348.697324 15.053679ADFG
40.4890468.798533 16.927683ABFG
40.4664478.991002 20.551236ABDG
40.4664058.991357 20.557976ADEG
40.4564649.074724 22.151919ABEG
50.5766258.0669 4.885100ACDFG
50.5746918.085305 5.195217ACEFG
50.5741128.0908 5.287950ABCFG
50.5349808.454345 11.562599ACDEG
50.5341908.46152 11.689210ABCEG
50.5248578.545865 13.185652ABCDG
50.5239508.554019 13.331103ADEFG
All Possible Results Section
ModelRoot
SizeR-SquaredMSECpModel
50.5040528.730959 16.521574ABEFG
50.5011208.756731 16.991729ABDFG
50.4664539.055876 22.550386ABDEG
60.5798238.095247 6.372266ACDEFG
60.5778298.114436 6.692043ABCDFG
60.5756838.135036 7.036172ABCEFG
60.5350258.515867 13.555333ABCDEG
60.5269698.589317 14.846961ABDEFG
60.35400310.03758 42.580795ABCDEF
70.5821458.132874 8.000000ABCDEFG
Plots Section
Appendix C
Initial Multiple Regression Model
Run Summary Section
ParameterValueParameterValue
Dependent VariableearningspercentRows Processed75
Number Ind. Variables4Rows Filtered Out0
Weight VariableNoneRows with X's Missing0
R20.5735Rows with Weight Missing0
Adj R20.5491Rows with Y Missing0
Coefficient of Variation0.3081Rows Used in Estimation75
Mean Square Error64.62592Sum of Weights75.000
Square Root of MSE8.039024Completion StatusNormal Completion
Ave Abs Pct Error51.466
Regression Equation Section
RegressionStandardT-ValueRejectPower
IndependentCoefficientErrorto test ProbH0 atof Test
Variableb(i)Sb(i)H0:B(i)=0Level5%?at 5%
Intercept45.91093.448413.3140.0000Yes1.0000
ftturn-0.12360.0332-3.7220.0004Yes0.9564
lotdampercar-12.17161.9442-6.2610.0000Yes1.0000
oshapercar-1.24630.4263-2.9230.0047Yes0.8220
sold0.00010.00000.0001.0000No0.0500
Estimated Model
45.9109493437341-.123625180145166*ftturn-12.1715683121402*lotdampercar-1.24625176987581*oshapercar+ 6.59602844882437E-05*sold
Regression Coefficient Section
IndependentRegressionStandardLowerUpperStandardized
VariableCoefficientError95% C.L.95% C.L.Coefficient
Intercept45.91093.448439.033352.78860.0000
ftturn-0.12360.0332-0.1899-0.0574-0.2966
lotdampercar-12.17161.9442-16.0491-8.2940-0.5431
oshapercar-1.24630.4263-2.0965-0.3960-0.2730
sold0.00010.00000.1328
Note: The T-Value used to calculate these confidence limits was 1.994.
Analysis of Variance Section
Sum ofMeanProbPower
SourceDFR2SquaresSquareF-RatioLevel(5%)
Intercept151068.7551068.75
Model40.57356081.8281520.45723.5270.00001.0000
Error700.42654523.81464.62592
Total(Adjusted)741.000010605.64143.3195
Normality Tests Section
TestTestProbReject H0
NameValueLevelAt Alpha = 20%?
Shapiro Wilk0.99470.989761No
Anderson Darling0.14690.966804No
D'Agostino Skewness0.33780.735526No
D'Agostino Kurtosis-0.16170.871531No
D'Agostino Omnibus0.14020.932278No
Multicollinearity Section
VarianceR2Diagonal
IndependentInflationVersusof X'X
VariableFactorOther I.V.'sToleranceInverse
ftturn1.04210.04040.95961.707224E-05
lotdampercar1.23490.19020.80985.848773E-02
oshapercar1.43090.30110.69892.81199E-03
sold0.00000
Predicted Values with Confidence Limits of Means
Standard95% Lower95% Upper
ActualPredictedError ofConf. LimitConf. Limit
Row earningspercent earningspercent Predicted of Mean of Mean
119.95630.6672.12126.43734.896
237.44031.8971.56328.77835.015
342.09327.2821.26124.76829.797
426.88426.3211.55523.22029.423
521.18123.1411.96119.23027.051
635.65338.9211.80835.31642.527
720.09117.3543.46210.44924.259
836.96529.1421.55026.05032.234
937.70532.0061.31929.37534.636
1016.36726.1842.90820.38431.983
111.91215.6932.70310.30121.085
1230.00325.4741.71122.06228.886
1327.03127.3883.67620.05734.719
1436.27331.8751.50528.87434.876
1515.57926.9841.44324.10529.863
1628.82519.1701.75215.67522.665
1719.6926.4602.9980.48212.439
1816.36529.0481.81025.43932.657
1942.30828.3131.57925.16531.462
2036.33432.4671.55229.37135.562
2126.96926.6182.06522.50030.736
2242.74835.3292.15431.03239.626
2325.80431.3591.45628.45634.263
24-4.0723.0632.955-2.8318.957
2514.51023.4482.12819.20527.691
2625.52727.2832.03523.22531.341
2713.25123.0482.68217.69928.396
2841.95742.0432.36137.33446.752
2929.69136.4972.27731.95641.037
3025.86130.0901.65226.79533.385
310.6447.1412.7891.57912.703
3234.22436.4732.36231.76341.184
3321.55529.8831.04827.79331.973
3421.53229.7711.59826.58332.958
3527.23331.6571.60328.46134.853
3623.74528.5491.83024.89832.200
3734.28833.8812.00529.88337.880
3826.53230.2971.77826.75133.844
3923.35218.0831.64814.79521.370
4033.50923.4821.05521.37725.587
4140.03119.7491.28117.19522.304
4236.72321.5711.57118.43724.705
4317.85120.2072.08216.05424.360
Predicted Values with Confidence Limits of Means
Standard95% Lower95% Upper
ActualPredictedError ofConf. LimitConf. Limit
Row earningspercent earningspercent Predicted of Mean of Mean
4422.24523.5992.26219.08828.110
45-4.072-2.9843.154-9.2733.306
4629.12332.0071.26729.48034.535
4725.80430.8981.17428.55633.240
4827.51723.8702.06519.75127.990
4932.30721.2051.24718.71723.693
5019.95631.7601.39928.96934.550
51-10.387-2.0183.338-8.6764.640
5214.51015.3882.45410.49320.282
5339.92134.4411.84730.75638.125
5441.95740.2532.31535.63744.870
5516.36721.9262.17117.59626.255
5639.92134.4291.63231.17437.685
5732.00427.8021.87224.06731.536
5827.51722.9472.12318.71227.182
5922.24521.8262.61416.61327.040
6010.13116.8032.26712.28021.325
6137.28530.7811.33228.12433.438
6226.75723.8651.10621.65926.072
6329.12332.3861.35429.68635.085
6434.13833.3272.43928.46438.191
6515.70426.6171.29924.02729.207
6641.09830.9861.42528.14533.827
6721.55530.7011.36927.97133.431
6811.64831.5481.36028.83634.260
6923.93724.5172.01920.49128.543
7013.47210.4843.2983.90617.063
7121.78416.0453.0869.88922.201
7242.47433.8241.48930.85436.794
7340.79033.5651.94829.68037.450
7433.56826.2492.42621.41131.086
7544.56242.7242.63637.46747.981
Predicted Values with Prediction Limits of Individuals
Standard95% Lower95% Upper
ActualPredictedError ofPred. LimitPred. Limit
Row earningspercent earningspercent Predicted of Individual of Individual
119.95630.6678.31414.08547.248
237.44031.8978.19015.56348.230
342.09327.2828.13711.05343.512
426.88426.3218.1889.99142.652
521.18123.1418.2756.63739.644
635.65338.9218.24022.48855.355
720.09117.3548.753-0.10334.811
836.96529.1428.18712.81445.471
937.70532.0068.14715.75848.253
1016.36726.1848.5499.13443.233
111.91215.6938.481-1.22332.608
1230.00325.4748.2199.08241.866
1327.03127.3888.8409.75845.018
1436.27331.8758.17915.56348.186
1515.57926.9848.16810.69443.274
1628.82519.1708.2282.76035.579
1719.6926.4608.580-10.65123.572
1816.36529.0488.24012.61345.482
1942.30828.3138.19311.97444.653
2036.33432.4678.18716.13748.796
2126.96926.6188.30010.06443.172
2242.74835.3298.32318.73051.928
2325.80431.3598.17015.06547.654
24-4.0723.0638.565-14.01920.146
2514.51023.4488.3166.86340.033
2625.52727.2838.29210.74443.822
2713.25123.0488.4756.14639.950
2841.95742.0438.37925.33258.753
2929.69136.4978.35519.83353.161
3025.86130.0908.20713.72246.458
310.6447.1418.509-9.83024.112
3234.22436.4738.37919.76253.184
3321.55529.8838.10713.71446.052
3421.53229.7718.19613.42346.118
3527.23331.6578.19715.30848.006
3623.74528.5498.24512.10544.993
3734.28833.8818.28517.35750.406
3826.53230.2978.23313.87646.718
3923.35218.0838.2061.71634.449
4033.50923.4828.1087.31139.653
4140.03119.7498.1403.51435.985
4236.72321.5718.1915.23437.908
4317.85120.2078.3043.64536.770
Predicted Values with Prediction Limits of Individuals
Standard95% Lower95% Upper
ActualPredictedError ofPred. LimitPred. Limit
Row earningspercent earningspercent Predicted of Individual of Individual
4422.24523.5998.3516.94340.255
45-4.072-2.9848.635-20.20714.239
4629.12332.0078.13815.77648.238
4725.80430.8988.12414.69447.101
4827.51723.8708.3007.31640.424
4932.30721.2058.1354.98037.430
5019.95631.7608.16015.48548.034
51-10.387-2.0188.705-19.37915.342
5214.51015.3888.405-1.37632.151
5339.92134.4418.24917.98950.892
5441.95740.2538.36623.56956.938
5516.36721.9268.3275.31838.533
5639.92134.4298.20318.06950.790
5732.00427.8028.25411.33944.264
5827.51722.9478.3156.36439.530
5922.24521.8268.4534.96738.686
6010.13116.8038.3530.14433.462
6137.28530.7818.14914.52947.033
6226.75723.8658.1157.68140.050
6329.12332.3868.15216.12748.645
6434.13833.3278.40116.57350.082
6515.70426.6178.14310.37642.858
6641.09830.9868.16414.70347.269
6721.55530.7018.15514.43746.965
6811.64831.5488.15315.28747.809
6923.93724.5178.2897.98641.048
7013.47210.4848.689-6.84627.815
7121.78416.0458.611-1.12933.219
7242.47433.8248.17617.51850.130
7340.79033.5658.27217.06850.063
7433.56826.2498.3979.50142.996
7544.56242.7248.46025.85159.597
Residual Report
AbsoluteSqrt(MSE)
ActualPredictedPercentWithout
Row earningspercent earningspercent ResidualErrorThis Row
119.95630.667-10.71153.6737.986
237.44031.8975.54314.8068.068
342.09327.28214.81035.1857.893
426.88426.3210.5622.0928.097
521.18123.141-1.9609.2538.093
635.65338.921-3.2699.1698.087
720.09117.3542.73713.6238.089
836.96529.1427.82221.1628.040
937.70532.0065.69915.1158.067
1016.36726.184-9.81659.9757.997
111.91215.693-13.781720.8337.903
1230.00325.4744.52915.0968.078
1327.03127.388-0.3571.3218.097
1436.27331.8754.39812.1258.079
1515.57926.984-11.40573.2097.976
1628.82519.1709.65633.4978.009
1719.6926.46013.23167.1937.913
1816.36529.048-12.68377.5027.944
1942.30828.31313.99533.0787.913
2036.33432.4673.86710.6448.083
2126.96926.6180.3511.3018.097
2242.74835.3297.41917.3568.044
2325.80431.359-5.55521.5298.068
24-4.0723.063-7.135175.2318.044
2514.51023.448-8.93861.6038.020
2625.52727.283-1.7566.8818.094
2713.25123.048-9.79773.9328.000
2841.95742.043-0.0860.2048.097
2929.69136.497-6.80622.9238.052
3025.86130.090-4.22916.3538.080
310.6447.141-6.4971008.1748.054
3234.22436.473-2.2496.5728.092
3321.55529.883-8.32838.6378.034
3421.53229.771-8.23938.2638.034
3527.23331.657-4.42416.2468.079
3623.74528.549-4.80420.2328.075
3734.28833.8810.4071.1868.097
3826.53230.297-3.76514.1908.084
3923.35218.0835.26922.5648.071
4033.50923.48210.02729.9248.005
4140.03119.74920.28250.6657.710
4236.72321.57115.15241.2617.881
4317.85120.207-2.35613.2018.092
Residual Report
AbsoluteSqrt(MSE)
ActualPredictedPercentWithout
Row earningspercent earningspercent ResidualErrorThis Row
4422.24523.599-1.3546.0888.095
45-4.072-2.984-1.08826.7218.096
4629.12332.007-2.8849.9018.089
4725.80430.898-5.09419.7418.073
4827.51723.8703.64713.2538.084
4932.30721.20511.10134.3627.983
5019.95631.760-11.80459.1507.967
51-10.387-2.018-8.36880.5698.021
5214.51015.388-0.8786.0528.096
5339.92134.4415.48013.7288.069
5441.95740.2531.7044.0618.094
5516.36721.926-5.55933.9628.067
5639.92134.4295.49113.7568.069
5732.00427.8024.20213.1308.080
5827.51722.9474.57016.6078.077
5922.24521.8260.4191.8828.097
6010.13116.803-6.67265.8628.054
6137.28530.7816.50417.4458.058
6226.75723.8652.89210.8088.089
6329.12332.386-3.26211.2018.087
6434.13833.3270.8102.3738.096
6515.70426.617-10.91369.4927.987
6641.09830.98610.11124.6038.002
6721.55530.701-9.14742.4348.020
6811.64831.548-19.899170.8347.724
6923.93724.517-0.5802.4248.097
7013.47210.4842.98722.1768.087
7121.78416.0455.73926.3468.062
7242.47433.8248.65020.3678.027
7340.79033.5657.22417.7118.047
7433.56826.2497.31921.8058.044
7544.56242.7241.8384.1248.094
Regression Diagnostics Section
StandardizedHat
RowResidualRStudentDiagonalCook's DDffitsCovRatio
1-1.3813-1.39050.06960.0285-0.38031.0059
20.70300.70040.03780.00390.13891.0780
31.86541.89980.02460.01750.30170.8538
40.07130.07080.03740.00000.01401.1160
5-0.2514-0.24970.05950.0008-0.06281.1374
6-0.4173-0.41480.05060.0019-0.09571.1178
70.37720.37490.18550.00650.17891.3059
80.99170.99160.03720.00760.19491.0399
90.71870.71620.02690.00290.11911.0642
10-1.3098-1.31660.13080.0516-0.51081.0921
11-1.8203-1.85160.11310.0845-0.66120.9507
120.57660.57380.04530.00320.12501.0991
13-0.0499-0.04960.20910.0001-0.02551.3584
140.55700.55420.03500.00230.10561.0891
15-1.4422-1.45360.03220.0139-0.26530.9550
161.23071.23530.04750.01510.27591.0113
171.77381.80210.13900.10160.72420.9917
18-1.6192-1.63860.05070.0280-0.37850.9353
191.77541.80380.03860.02530.36130.8877
200.49030.48760.03730.00190.09601.0972
210.04520.04480.06600.00000.01191.1503
220.95790.95740.07180.01420.26631.0838
23-0.7027-0.70010.03280.0033-0.12891.0724
24-0.9544-0.95370.13510.0285-0.37701.1638
25-1.1530-1.15580.07000.0200-0.31721.0499
26-0.2258-0.22430.06410.0007-0.05871.1440
27-1.2927-1.29900.11130.0418-0.45971.0716
28-0.0111-0.01110.08630.0000-0.00341.1760
29-0.8828-0.88140.08020.0136-0.26031.1047
30-0.5375-0.53480.04220.0025-0.11231.0990
31-0.8616-0.86000.12030.0203-0.31811.1582
32-0.2927-0.29080.08630.0016-0.08941.1689
33-1.0449-1.04560.01700.0038-0.13751.0105
34-1.0457-1.04640.03950.0090-0.21231.0341
35-0.5616-0.55880.03970.0026-0.11371.0941
36-0.6137-0.61100.05180.0041-0.14291.1032
370.05220.05180.06220.00000.01341.1456
38-0.4802-0.47760.04890.0024-0.10831.1114
390.66970.66700.04200.00390.13971.0863
401.25821.26360.01720.00560.16740.9753
412.55562.66460.02540.03400.43010.6757
421.92191.96050.03820.02930.39080.8520
43-0.3035-0.30150.06710.0013-0.08091.1443
44-0.1756-0.17430.07920.0005-0.05111.1644
Regression Diagnostics Section
StandardizedHat
RowResidualRStudentDiagonalCook's DDffitsCovRatio
45-0.1471-0.14610.15390.0008-0.06231.2681
46-0.3632-0.36100.02490.0007-0.05761.0916
47-0.6405-0.63780.02130.0018-0.09421.0662
480.46940.46680.06600.00310.12411.1326
491.39781.40760.02410.00960.22110.9558
50-1.4911-1.50450.03030.0139-0.26590.9430
51-1.1443-1.14690.17240.0546-0.52351.1815
52-0.1147-0.11390.09320.0003-0.03651.1839
530.70050.69790.05280.00550.16481.0953
540.22130.21980.08290.00090.06611.1676
55-0.7181-0.71560.07290.0081-0.20071.1170
560.69760.69500.04120.00420.14411.0824
570.53750.53480.05430.00330.12811.1130
580.58940.58660.06980.00520.16061.1268
590.05510.05470.10570.00010.01881.2014
60-0.8651-0.86350.07960.0129-0.25391.1064
610.82050.81850.02750.00380.13751.0528
620.36320.36090.01890.00050.05011.0851
63-0.4117-0.40920.02830.0010-0.06991.0926
640.10580.10500.09200.00020.03341.1826
65-1.3756-1.38450.02610.0101-0.22660.9621
661.27801.28390.03140.01060.23120.9859
67-1.1546-1.15740.02900.0080-0.20001.0052
68-2.5116-2.61410.02860.0372-0.44870.6899
69-0.0746-0.07400.06310.0001-0.01921.1465
700.40750.40510.16830.00670.18221.2769
710.77320.77090.14740.02070.32061.2075
721.09501.09660.03430.00850.20671.0207
730.92630.92530.05870.01070.23111.0734
740.95500.95440.09100.01830.30201.1072
750.24200.24030.10750.00140.08341.1990
Plots Section
Appendix D
Final Multiple Regression Model
Run Summary Section
ParameterValueParameterValue
Dependent VariableearningspercentRows Processed75
Number Ind. Variables4Rows Filtered Out0
Weight VariableNoneRows with X's Missing0
R20.5968Rows with Weight Missing0
Adj R20.5738Rows with Y Missing0
Coefficient of Variation0.2995Rows Used in Estimation75
Mean Square Error61.08409Sum of Weights75.000
Square Root of MSE7.815631Completion StatusNormal Completion
Ave Abs Pct Error47.764
Regression Equation Section
RegressionStandardT-ValueRejectPower
IndependentCoefficientErrorto test ProbH0 atof Test
Variableb(i)Sb(i)H0:B(i)=0Level5%?at 5%
Intercept51.27132.873517.8430.0000Yes1.0000
ftturn-0.13030.0320-4.0680.0001Yes0.9799
inverse_sold-82079.578032760.1107-2.5050.0146Yes0.6953
lotdampercar-11.47021.7749-6.4630.0000Yes1.0000
oshapercar-1.15250.3938-2.9270.0046Yes0.8229
Estimated Model
51.2712784440518-.130345474537923*ftturn-82079.5780151717*inverse_sold-11.4702106246791*lotdampercar-1.15251248433065*oshapercar
Regression Coefficient Section
IndependentRegressionStandardLowerUpperStandardized
VariableCoefficientError95% C.L.95% C.L.Coefficient
Intercept51.27132.873545.540257.00240.0000
ftturn-0.13030.0320-0.1943-0.0664-0.3127
inverse_sold-82079.578032760.1107-147417.5586-16741.5975-0.2085
lotdampercar-11.47021.7749-15.0101-7.9303-0.5118
oshapercar-1.15250.3938-1.9379-0.3672-0.2524
Note: The T-Value used to calculate these confidence limits was 1.994.
Analysis of Variance Section
Sum ofMeanProbPower
SourceDFR2SquaresSquareF-RatioLevel(5%)
Intercept151068.7551068.75
Model40.59686329.7551582.43925.9060.00001.0000
Error700.40324275.88661.08409
Total(Adjusted)741.000010605.64143.3195
Normality Tests Section
TestTestProbReject H0
NameValueLevelAt Alpha = 20%?
Shapiro Wilk0.99060.858303No
Anderson Darling0.22020.834898No
D'Agostino Skewness0.37910.704620No
D'Agostino Kurtosis0.22960.818433No
D'Agostino Omnibus0.19640.906464No
Multicollinearity Section
VarianceR2Diagonal
IndependentInflationVersusof X'X
VariableFactorOther I.V.'sToleranceInverse
ftturn1.02610.02540.97461.680963E-05
inverse_sold1.20210.16810.83191.756963E+07
lotdampercar1.08880.08160.91845.157117E-02
oshapercar1.29160.22580.77422.538321E-03
Predicted Values with Confidence Limits of Means
Standard95% Lower95% Upper
ActualPredictedError ofConf. LimitConf. Limit
Row earningspercent earningspercent Predicted of Mean of Mean
119.95630.1121.31127.49832.726
237.44032.4151.53229.36135.470
342.09328.4631.33025.81031.116
426.88426.2001.49923.21129.189
521.18124.5072.02320.47328.541
635.65338.8431.63635.58042.106
720.09116.2632.69210.89521.632
836.96529.3971.43826.52932.265
937.70532.6431.32130.00935.277
1016.36724.4261.74020.95627.897
111.91210.6963.6053.50717.886
1230.00326.0231.65022.73329.314
1327.03125.1992.55920.09630.302
1436.27332.4471.48529.48635.408
1515.57925.8191.47222.88428.755
1628.82520.0001.72616.55723.442
1719.6928.5942.6843.24213.947
1816.36525.5892.45720.69030.488
1942.30829.1761.59325.99832.354
2036.33432.7591.32130.12535.393
2126.96926.9491.77323.41330.484
2242.74835.4321.85931.72439.140
2325.80431.6061.23629.14134.071
24-4.0724.9902.711-0.41610.397
2514.51024.5562.06920.43028.683
2625.52726.6871.57623.54429.831
2713.25124.9722.76719.45430.490
2841.95743.1042.32538.46847.741
2929.69136.8672.03132.81640.918
3025.86130.5711.47527.62933.513
310.6447.0602.7111.65212.467
3234.22435.2331.47732.28838.178
3321.55530.7971.10228.59932.995
3421.53230.0931.46327.17433.011
3527.23331.8551.40929.04534.665
3623.74527.7571.78424.19931.315
3734.28833.8171.85130.12637.508
3826.53229.4971.60726.29232.701
3923.35219.6051.43016.75222.458
4033.50924.6341.13922.36326.906
4140.03121.0511.40018.25823.845
4236.72318.3462.21213.93322.758
4317.85120.1442.00816.13924.149
Predicted Values with Confidence Limits of Means
Standard95% Lower95% Upper
ActualPredictedError ofConf. LimitConf. Limit
Row earningspercent earningspercent Predicted of Mean of Mean
4422.24524.0112.20419.61628.406
45-4.072-1.2393.077-7.3764.898
4629.12332.9381.26530.41435.462
4725.80431.7221.20329.32334.121
4827.51723.8571.98919.88927.824
4932.30722.4601.17920.10824.812
5019.95632.1251.23329.66734.583
51-10.387-7.8504.289-16.4040.705
5214.51015.2792.38010.53220.026
5339.92135.2461.78131.69438.799
5441.95741.3422.22736.90145.784
5516.36721.7951.66118.48225.109
5639.92135.5921.66132.27938.905
5732.00428.8871.89825.10232.671
5827.51723.5312.08519.37427.689
5922.24520.9212.52215.89225.951
6010.13115.2932.32110.66419.922
6137.28531.4471.33528.78434.110
6226.75725.0561.06922.92527.187
6329.12332.8791.27830.33135.427
6434.13828.7783.12322.54935.007
6515.70428.1531.40925.34330.963
6641.09832.0151.43329.15734.874
6721.55531.4351.19329.05633.813
6811.64831.9631.23529.50034.427
6923.93721.7592.29017.19126.327
7013.47212.7122.9426.84418.580
7121.78417.6593.09311.49123.827
7242.47434.4061.47531.46437.347
7340.79028.6663.06122.56134.771
7433.56826.9022.36122.19331.612
7544.56242.1412.43537.28446.998
Predicted Values with Prediction Limits of Individuals
Standard95% Lower95% Upper
ActualPredictedError ofPred. LimitPred. Limit
Row earningspercent earningspercent Predicted of Individual of Individual
119.95630.1127.92514.30745.918
237.44032.4157.96416.53148.300
342.09328.4637.92812.65144.275
426.88426.2007.95810.32842.072
521.18124.5078.0738.40540.608
635.65338.8437.98522.91754.769
720.09116.2638.266-0.22332.750
836.96529.3977.94713.54845.246
937.70532.6437.92616.83448.452
1016.36724.4268.0078.45740.396
111.91210.6968.607-6.47027.862
1230.00326.0237.98810.09241.955
1327.03125.1998.2248.79741.601
1436.27332.4477.95516.58048.313
1515.57925.8197.9539.95841.681
1628.82520.0008.0044.03635.963
1719.6928.5948.264-7.88725.076
1816.36525.5898.1939.24941.929
1942.30829.1767.97613.26745.084
2036.33432.7597.92616.95048.568
2126.96926.9498.01410.96542.932
2242.74835.4328.03419.40951.455
2325.80431.6067.91315.82547.388
24-4.0724.9908.272-11.50821.489
2514.51024.5568.0858.43240.681
2625.52726.6877.97310.78642.589
2713.25124.9728.2918.43641.508
2841.95743.1048.15426.84159.367
2929.69136.8678.07520.76152.972
3025.86130.5717.95414.70846.434
310.6447.0608.273-9.44023.559
3234.22435.2337.95419.37051.097
3321.55530.7977.89315.05546.539
3421.53230.0937.95114.23445.951
3527.23331.8557.94216.01647.694
3623.74527.7578.01711.76843.746
3734.28833.8178.03217.79849.836
3826.53229.4977.97913.58345.411
3923.35219.6057.9453.75835.452
4033.50924.6347.8988.88240.387
4140.03121.0517.9405.21536.887
4236.72318.3468.1232.14534.546
4317.85120.1448.0694.05036.238
Predicted Values with Prediction Limits of Individuals
Standard95% Lower95% Upper
ActualPredictedError ofPred. LimitPred. Limit
Row earningspercent earningspercent Predicted of Individual of Individual
4422.24524.0118.1207.81540.206
45-4.072-1.2398.400-17.99215.513
4629.12332.9387.91717.14748.729
4725.80431.7227.90815.95147.494
4827.51723.8578.0657.77239.941
4932.30722.4607.9046.69638.224
5019.95632.1257.91216.34547.905
51-10.387-7.8508.915-25.6309.931
5214.51015.2798.170-1.01531.573
5339.92135.2468.01619.25951.234
5441.95741.3428.12725.13457.550
5516.36721.7957.9905.85937.731
5639.92135.5927.99019.65651.528
5732.00428.8878.04312.84644.927
5827.51723.5318.0897.39939.664
5922.24520.9218.2124.54237.301
6010.13115.2938.153-0.96831.553
6137.28531.4477.92915.63447.261
6226.75725.0567.8889.32340.789
6329.12332.8797.91917.08448.673
6434.13828.7788.41611.99245.564
6515.70428.1537.94212.31443.992
6641.09832.0157.94616.16847.863
6721.55531.4357.90615.66647.203
6811.64831.9637.91316.18247.745
6923.93721.7598.1445.51538.002
7013.47212.7128.351-3.94429.368
7121.78417.6598.4050.89534.423
7242.47434.4067.95418.54350.269
7340.79028.6668.39411.92545.407
7433.56826.9028.16510.61943.186
7544.56242.1418.18625.81458.468
Residual Report
AbsoluteSqrt(MSE)
ActualPredictedPercentWithout
Row earningspercent earningspercent ResidualErrorThis Row
119.95630.112-10.15750.8967.774
237.44032.4155.02513.4207.848
342.09328.46313.62932.3807.694
426.88426.2000.6832.5427.872
521.18124.507-3.32615.7037.861
635.65338.843-3.1908.9487.862
720.09116.2633.82719.0517.857
836.96529.3977.56820.4737.817
937.70532.6435.06213.4257.848
1016.36724.426-8.05949.2407.809
111.91210.696-8.784459.4817.781
1230.00326.0233.98013.2647.857
1327.03125.1991.8316.7767.869
1436.27332.4473.82610.5487.858
1515.57925.819-10.24165.7357.771
1628.82520.0008.82630.6177.796
1719.6928.59411.09756.3557.742
1816.36525.589-9.22456.3677.785
1942.30829.17613.13231.0407.705
2036.33432.7593.5759.8407.860
2126.96926.9490.0200.0747.872
2242.74835.4327.31617.1147.820
2325.80431.606-5.80222.4857.840
24-4.0724.990-9.062222.5617.786
2514.51024.556-10.04769.2437.772
2625.52726.687-1.1614.5487.871
2713.25124.972-11.72188.4557.726
2841.95743.104-1.1472.7347.871
2929.69136.867-7.17624.1707.821
3025.86130.571-4.71018.2127.851
310.6447.060-6.415995.5437.829
3234.22435.233-1.0092.9487.871
3321.55530.797-9.24242.8787.791
3421.53230.093-8.56139.7597.802
3527.23331.855-4.62216.9737.852
3623.74527.757-4.01216.8977.856
3734.28833.8170.4711.3747.872
3826.53229.497-2.96411.1737.864
3923.35219.6053.74616.0447.859
4033.50924.6348.87526.4847.798
4140.03121.05118.98047.4137.522
4236.72318.34618.37750.0437.527
4317.85120.144-2.29312.8457.867
Residual Report
AbsoluteSqrt(MSE)
ActualPredictedPercentWithout
Row earningspercent earningspercent ResidualErrorThis Row
4422.24524.011-1.7667.9387.869
45-4.072-1.239-2.83269.5607.863
4629.12332.938-3.81413.0977.858
4725.80431.722-5.91822.9367.839
4827.51723.8573.66113.3037.859
4932.30722.4609.84730.4797.780
5019.95632.125-12.16960.9827.731
51-10.387-7.850-2.53724.4267.864
5214.51015.279-0.7695.3037.871
5339.92135.2464.67511.7107.851
5441.95741.3420.6151.4667.872
5516.36721.795-5.42833.1637.844
5639.92135.5924.32910.8447.854
5732.00428.8873.1179.7417.863
5827.51723.5313.98614.4847.856
5922.24520.9211.3245.9507.870
6010.13115.293-5.16250.9587.845
6137.28531.4475.83815.6587.840
6226.75725.0561.7016.3587.869
6329.12332.879-3.75512.8947.859
6434.13828.7785.36015.7007.841
6515.70428.153-12.44979.2747.723
6641.09832.0159.08222.0997.793
6721.55531.435-9.88045.8367.780
6811.64831.963-20.315174.4017.472
6923.93721.7592.1789.0997.867
7013.47212.7120.7605.6397.871
7121.78417.6594.12518.9367.853
7242.47434.4068.06818.9967.810
7340.79028.66612.12429.7237.711
7433.56826.9026.66619.8577.827
7544.56242.1412.4215.4327.866
Regression Diagnostics Section
StandardizedHat
RowResidualRStudentDiagonalCook's DDffitsCovRatio
1-1.3182-1.32530.02810.0101-0.22540.9751
20.65560.65290.03840.00340.13051.0836
31.76971.79770.02900.01870.31050.8803
40.08910.08850.03680.00010.01731.1150
5-0.4406-0.43800.06700.0028-0.11731.1358
6-0.4174-0.41500.04380.0016-0.08881.1099
70.52160.51890.11860.00730.19041.1957
80.98510.98490.03380.00680.18431.0373
90.65710.65440.02860.00250.11221.0725
10-1.0577-1.05860.04960.0117-0.24181.0431
11-1.2667-1.27230.21270.0867-0.66141.2155
120.52090.51820.04460.00250.11191.1031
130.24800.24630.10720.00150.08531.1983
140.49860.49590.03610.00190.09601.0952
15-1.3342-1.34180.03550.0131-0.25730.9795
161.15781.16070.04880.01370.26281.0256
171.51181.52610.11790.06110.55801.0319
18-1.2432-1.24820.09880.0339-0.41331.0664
191.71631.74100.04160.02550.36250.9043
200.46410.46150.02850.00130.07911.0893
210.00260.00260.05140.00000.00061.1329
220.96370.96320.05660.01110.23591.0655
23-0.7518-0.74950.02500.0029-0.12001.0584
24-1.2362-1.24100.12030.0418-0.45891.0939
25-1.3330-1.34060.07010.0268-0.36811.0162
26-0.1517-0.15060.04070.0002-0.03101.1183
27-1.6035-1.62210.12530.0737-0.61401.0189
28-0.1537-0.15260.08850.0005-0.04761.1769
29-0.9509-0.95020.06750.0131-0.25571.0799
30-0.6136-0.61090.03560.0028-0.11741.0846
31-0.8752-0.87370.12040.0210-0.32321.1562
32-0.1315-0.13050.03570.0001-0.02511.1130
33-1.1945-1.19820.01990.0058-0.17060.9891
34-1.1151-1.11700.03510.0090-0.21291.0182
35-0.6013-0.59850.03250.0024-0.10971.0823
36-0.5273-0.52450.05210.0031-0.12301.1113
370.06200.06160.05610.00000.01501.1381
38-0.3876-0.38520.04230.0013-0.08091.1100
390.48760.48490.03350.00160.09031.0931
401.14781.15040.02120.00570.16950.9984
412.46842.56490.03210.04040.46720.7041
422.45162.54580.08010.10470.75130.7457
43-0.3036-0.30160.06600.0013-0.08021.1430
44-0.2355-0.23390.07950.0010-0.06871.1628
Regression Diagnostics Section
StandardizedHat
RowResidualRStudentDiagonalCook's DDffitsCovRatio
45-0.3942-0.39180.15500.0057-0.16781.2577
46-0.4946-0.49190.02620.0013-0.08071.0844
47-0.7664-0.76410.02370.0028-0.11901.0553
480.48430.48160.06480.00320.12681.1299
491.27441.28020.02280.00760.19540.9778
50-1.5768-1.59400.02490.0127-0.25460.9197
51-0.3883-0.38590.30120.0130-0.25341.5212
52-0.1034-0.10260.09270.0002-0.03281.1835
530.61430.61150.05190.00410.14311.1032
540.08210.08150.08120.00010.02421.1690
55-0.7107-0.70820.04520.0048-0.15411.0854
560.56690.56410.04520.00300.12271.0998
570.41120.40870.05900.00210.10231.1282
580.52910.52640.07110.00430.14571.1339
590.17890.17770.10410.00070.06061.1967
60-0.6917-0.68910.08820.0093-0.21431.1388
610.75810.75580.02920.00350.13101.0622
620.21970.21820.01870.00020.03011.0913
63-0.4870-0.48440.02670.0013-0.08031.0855
640.74810.74570.15970.02130.32511.2285
65-1.6194-1.63880.03250.0176-0.30040.9177
661.18211.18550.03360.00970.22111.0053
67-1.2791-1.28500.02330.0078-0.19840.9775
68-2.6323-2.75330.02500.0355-0.44060.6544
690.29150.28960.08590.00160.08881.1684
700.10490.10420.14170.00040.04231.2510
710.57470.57190.15660.01230.24641.2443
721.05121.05200.03560.00820.20221.0291
731.68591.70880.15340.10300.72731.0317
740.89470.89340.09130.01610.28321.1165
750.32590.32390.09710.00230.10621.1812
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