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Module 04 Session Long Project

The data taken for analysis for this module is from “From Business Week’s analysis of the S&P 500 for 2004”. The Industry Ranking S&P 500 is based on three factors Market Value (MarketValue, MvOneYearTotalReturn, and MvThreeYearTotalReturn), Sales (Sales, SalesChangeFrom2002, and Sales3YrAverageChange) and Profitability (Profitability, ProfitChangeFrom2002, and Profit3YrAverageChange).

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Descriptive Statistics and Frequency Tabulations

Table 1 shows the descriptive statistics of all variables. From table 1, it can be seen that all the variables are highly positively skewed (i.e. skewed to left) as the value of skewness coefficient is greater than zero for all variables. The positive skewness is also confirmed from the mean, median and mode values. The mean value for all the variables is greater than median values and median values for all the variables are greater than mode values. The Histograms for all the variables confirms positive skewness as the right tail for all the variables are longer.

Table 1: Descriptive Statistics

OverallSP500Rank_04
MarketValue
MvOneYearTotalReturn
MvThreeYearTotalReturn
Sales
SalesChangeFrom2002
Sales3YrAverageChange
Profitability
ProfitChangeFrom2002
Profit3YrAverageChange
N
Valid
483
488
479
312
486
408
312
428
264
251
Missing
236
231
240
407
233
311
407
291
455
468
Mean
245.56
21321.459
57.267
51.984
13277.491
14.85
10.833
1115.366
93.09
25.960
Median
243.00
9251.550
45.400
36.350
6316.000
11.00
7.200
478.000
27.00
15.700
Mode
28
4021.5a
25.1a
8.0a
679.6a
11
3.3
109.8a
9a
10.4
Std. Deviation
143.509
39064.4620
50.4681
51.6895
23919.9416
22.125
11.2732
2108.2942
288.293
35.9557
Skewness
.021
4.663
5.107
2.403
5.793
9.586
2.236
5.148
7.530
4.457
Std. Error of Skewness
.111
.111
.112
.138
.111
.121
.138
.118
.150
.154
Range
493
325661.2
682.8
395.4
258577.1
352
70.3
20957.1
2834
302.4
Minimum
1
867.6
.3
.1
103.9
0
.0
2.9
0
.2
Maximum
494
326528.8
683.1
395.5
258681.0
352
70.3
20960.0
2834
302.6
a. Multiple modes exist. The smallest value is shown

Histograms

Scatterplots

The Scatter plots for MarketValue, MvOneYearTotalReturn, MvThreeYearTotalReturn, Sales and Profitability are drawn against OverallSP500Rank_04. Except for MvOneYearTotalReturn, all other variables show a decreasing linear trend against OverallSP500Rank_04.

Correlation matrix

Table 2 shows the Correlation matrix of all variables. The strongest correlation is between variables MarketValue and Profitability. The weakest correlation is between variables ProfitChangeFrom2002 and Profitability. OverallSP500Rank_04 has strongest correlation is with MvThreeYearTotalReturn and weakest correlation with ProfitChangeFrom2002. Most of the correlations for the variables OverallSP500Rank_04 with other variables are significant at 95% significance level (p-value less than 0.05), except two that are ProfitChangeFrom2002 and Profit3YrAverageChange (p-value greater than 0.05).

Table 2: Correlations

OverallSP500Rank_04
MarketValue
MvOneYearTotalReturn
MvThreeYearTotalReturn
Sales
SalesChangeFrom2002
Sales3YrAverageChange
Profitability
ProfitChangeFrom2002
Profit3YrAverageChange
OverallSP500Rank_04
Pearson Correlation
1.000
-.296**
.125**
-.329**
-.235**
-.183**
-.305**
-.292**
-.029
.095
Sig. (2-tailed)

.000
.006
.000
.000
.000
.000
.000
.636
.137
N
483.000
483
475
309
483
405
312
427
262
249
MarketValue
Pearson Correlation
-.296**
1.000
-.129**
-.101
.664**
.000
-.014
.873**
.047
-.026
Sig. (2-tailed)
.000

.005
.074
.000
.993
.800
.000
.446
.677
N
483
488.000
479
312
486
408
312
428
264
251
MvOneYearTotalReturn
Pearson Correlation
.125**
-.129**
1.000
.171**
-.103*
.108*
.087
-.107*
.049
-.031
Sig. (2-tailed)
.006
.005

.003
.025
.030
.126
.028
.431
.626
N
475
479
479.000
308
478
401
307
421
257
245
MvThreeYearTotalReturn
Pearson Correlation
-.329**
-.101
.171**
1.000
-.120*
.126*
.172*
-.109
.022
-.132
Sig. (2-tailed)
.000
.074
.003

.035
.038
.011
.060
.773
.097
N
309
312
308
312.000
311
273
220
301
171
160
Sales
Pearson Correlation
-.235**
.664**
-.103*
-.120*
1.000
-.010
.010
.709**
.063
-.009
Sig. (2-tailed)
.000
.000
.025
.035

.846
.854
.000
.305
.888
N
483
486
478
311
486.000
408
312
428
264
251
SalesChangeFrom2002
Pearson Correlation
-.183**
.000
.108*
.126*
-.010
1.000
.314**
-.037
-.008
-.016
Sig. (2-tailed)
.000
.993
.030
.038
.846

.000
.480
.910
.816
N
405
408
401
273
408
408.000
300
372
223
210
Sales3YrAverageChange
Pearson Correlation
-.305**
-.014
.087
.172*
.010
.314**
1.000
-.044
-.016
.022
Sig. (2-tailed)
.000
.800
.126
.011
.854
.000

.450
.843
.788
N
312
312
307
220
312
300
312.000
295
166
158
Profitability
Pearson Correlation
-.292**
.873**
-.107*
-.109
.709**
-.037
-.044
1.000
-.002
.015
Sig. (2-tailed)
.000
.000
.028
.060
.000
.480
.450

.974
.821
N
427
428
421
301
428
372
295
428.000
230
221
ProfitChangeFrom2002
Pearson Correlation
-.029
.047
.049
.022
.063
-.008
-.016
-.002
1.000
.031
Sig. (2-tailed)
.636
.446
.431
.773
.305
.910
.843
.974

.669
N
262
264
257
171
264
223
166
230
264.000
198
Profit3YrAverageChange
Pearson Correlation
.095
-.026
-.031
-.132
-.009
-.016
.022
.015
.031
1.000
Sig. (2-tailed)
.137
.677
.626
.097
.888
.816
.788
.821
.669

N
249
251
245
160
251
210
158
221
198
251.000
**. Correlation is significant at the 0.01 level (2-tailed).

*. Correlation is significant at the 0.05 level (2-tailed).

Regression Analysis

The variables MvThreeYearTotalReturn, Sales3YrAverageChange, MarketValue, and Profitability have the highest correlations with OverallSP500Rank_04.

The regression analysis gives a model for predicting dependent variables based on independent variables. The regression analysis gives three types of statistics in SPSS:

·         The coefficient of determination, designated as R Square ( R2) that tells the proportion of variance in the dependent variable that can be accounted for by the independent variable.

·         An ANOVA table for the regression equation for testing null hypothesis that R2 in the population equals zero, and allows us to decide whether or not the linear model significantly fits the data at the p<.05 level.

·         The output (coefficients for intercepts and slope) that provides the information needed to construct the regression (prediction) equation.

1.         Regression: OverallSP500Rank_04 (DV) and MvThreeYearTotalReturn (IV)

The regression analysis for OverallSP500Rank_04 (DV) and MvThreeYearTotalReturn (IV) is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.108 implies that the MvThreeYearTotalReturn (IV) can account for 10.8% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 240.811 – 0.816(MvThreeYearTotalReturn)

Variables Entered/Removedb
Model
Variables Entered
Variables Removed
Method
1
MvThreeYearTotalReturna
.
Enter
a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.329a
.108
.105
120.307
a. Predictors: (Constant), MvThreeYearTotalReturn

ANOVAb
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
539735.167
1
539735.167
37.291
.000a
Residual
4443418.587
307
14473.676

Total
4983153.754
308

a. Predictors: (Constant), MvThreeYearTotalReturn

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
240.811
9.731

24.747
.000
MvThreeYearTotalReturn
-.816
.134
-.329
-6.107
.000
a. Dependent Variable: OverallSP500Rank_04

2.       Regression: OverallSP500Rank_04 (DV) and Sales3YrAverageChange (IV)

The regression analysis for OverallSP500Rank_04 (DV) and Sales3YrAverageChange (IV) is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.093 implies that the Sales3YrAverageChange (IV) can account for 9.3% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 231.106 – 3.527(Sales3YrAverageChange)

Variables Entered/Removedb
Model
Variables Entered
Variables Removed
Method
1
Sales3YrAverageChangea
.
Enter
a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.305a
.093
.090
124.383
a. Predictors: (Constant), Sales3YrAverageChange

ANOVAb
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
491538.189
1
491538.189
31.772
.000a
Residual
4796012.927
310
15471.009

Total
5287551.115
311

a. Predictors: (Constant), Sales3YrAverageChange

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
231.106
9.773

23.646
.000
Sales3YrAverageChange
-3.527
.626
-.305
-5.637
.000
a. Dependent Variable: OverallSP500Rank_04

3.       Regression: OverallSP500Rank_04 (DV) and MarketValue (IV)

The regression analysis for OverallSP500Rank_04 (DV) and MarketValue is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.088 implies that the MarketValue can account for 8.8% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 268.786 – 0.001(MarketValue)

Variables Entered/Removedb
Model
Variables Entered
Variables Removed
Method
1
MarketValuea
.
Enter
a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.296a
.088
.086
137.216
a. Predictors: (Constant), MarketValue

ANOVAb
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
870326.947
1
870326.947
46.224
.000a
Residual
9056401.877
481
18828.278

Total
9926728.824
482

a. Predictors: (Constant), MarketValue

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
268.786
7.117

37.768
.000
MarketValue
-.001
.000
-.296
-6.799
.000
a. Dependent Variable: OverallSP500Rank_04

4.       Regression: OverallSP500Rank_04 (DV) and Profitability (IV)

The regression analysis for OverallSP500Rank_04 (DV) and Profitability is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.085 implies that the Profitability can account for 8.5% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 239.049 – 0.018(Profitability)

Variables Entered/Removedb
Model
Variables Entered
Variables Removed
Method
1
Profitabilitya
.
Enter
a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.292a
.085
.083
124.606
a. Predictors: (Constant), Profitability

ANOVAb
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
612846.265
1
612846.265
39.470
.000a
Residual
6598854.601
425
15526.717

Total
7211700.867
426

a. Predictors: (Constant), Profitability

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
239.049
6.819

35.058
.000
Profitability
-.018
.003
-.292
-6.283
.000
a. Dependent Variable: OverallSP500Rank_04

Multiple Regression: (Taking four Independent Variables that have highest Correlation with OverallSP500Rank_04)

The regression analysis for OverallSP500Rank_04 (DV) and MvThreeYearTotalReturn, Sales3YrAverageChange, MarketValue, and Profitability (IVs) is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.330 implies that the MvThreeYearTotalReturn, Sales3YrAverageChange, MarketValue, and Profitability (IVs) can account for 33% of variance in the OverallSP500Rank_04 (DV).

The linear regression equation will be:

‘OverallSP500Rank_04 = 247.781 – 0.591(MvThreeYearTotalReturn) – 3.329(Sales3YrAverageChange) – 0.013(Profitability)

Variables Entered/Removedb
Model
Variables Entered
Variables Removed
Method
1
Profitability, Sales3YrAverageChange, MvThreeYearTotalReturn, MarketValuea
.
Enter
a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.574a
.330
.317
93.252
a. Predictors: (Constant), Profitability, Sales3YrAverageChange, MvThreeYearTotalReturn, MarketValue

ANOVAb
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
894689.681
4
223672.420
25.722
.000a
Residual
1817443.777
209
8695.903

Total
2712133.458
213

a. Predictors: (Constant), Profitability, Sales3YrAverageChange, MvThreeYearTotalReturn, MarketValue
b. Dependent Variable: OverallSP500Rank_04

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
247.781
11.181

22.161
.000
MvThreeYearTotalReturn
-.591
.117
-.294
-5.037
.000
Sales3YrAverageChange
-3.329
.542
-.353
-6.137
.000
MarketValue
.000
.000
-.116
-.838
.403
Profitability
-.013
.008
-.217
-1.563
.119
a. Dependent Variable: OverallSP500Rank_04

We can leave variable MarketValue, as for four variable regression analysis, MarketValue has not significant effect on linear regression equation.

Multiple Regression (Taking all Independent Variables)

The regression analysis for OverallSP500Rank_04 (DV) and Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, and MarketValue (IVs)  is significant as the sig value in ANOVA table is less than 0.05. The value of the coefficient of determination 0.502 implies all the independent variables can account for 50.2% of variance in the OverallSP500Rank_04 (DV).

Variables Entered/Removedb
Model
Variables Entered
Variables Removed
Method
1
Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, MarketValuea
.
Enter
a. All requested variables entered.

b. Dependent Variable: OverallSP500Rank_04

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.708a
.502
.440
84.217
a. Predictors: (Constant), Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, MarketValue

ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.

1
Regression
520912.573
9
57879.175
8.161
.000a

Residual
517747.981
73
7092.438

Total
1038660.554
82

a. Predictors: (Constant), Profit3YrAverageChange, SalesChangeFrom2002, Profitability, MvThreeYearTotalReturn, ProfitChangeFrom2002, Sales3YrAverageChange, MvOneYearTotalReturn, Sales, MarketValue

b. Dependent Variable: OverallSP500Rank_04

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
331.979
28.440

11.673
.000
MarketValue
.003
.002
.324
1.600
.114
MvOneYearTotalReturn
-.955
.402
-.228
-2.373
.020
MvThreeYearTotalReturn
-.500
.170
-.285
-2.951
.004
Sales
.001
.001
.259
2.244
.028
SalesChangeFrom2002
-.714
.756
-.090
-.944
.348
Sales3YrAverageChange
-4.377
1.124
-.377
-3.896
.000
Profitability
-.135
.036
-.773
-3.703
.000
ProfitChangeFrom2002
-.051
.040
-.141
-1.283
.203
Profit3YrAverageChange
.158
.270
.051
.585
.561
a. Dependent Variable: OverallSP500Rank_04

We can leave variable MarketValue, SalesChangeFrom2002, ProfitChangeFrom2002, and Profit3YrAverageChange as these variables has not significant effect on linear regression equation.

 

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