Research Question

:

What are the factors that influence the economic performance of a company?

Economic performance is measured by the return on capital employed.

Methodology

:

Multiple Regression Analysis

Dataset

:

After filtering    40 cases read from the input data file
1                            Multiple Regression Analysis
Number of variables = 13

Number of cases = 40

General statistics

    Variable                    Standard                       Range
     Number     Sum        Average     Deviation        Max            	 Min    Variable name

       3    1220.00000    30.50000      22.94028       91.0000     	   .0000      GEARRAT 
       4    6107.00000   152.67500      83.14257      346.0000   	   .0000       CAPINT 
       5    1501.00000    37.52500      99.04415      625.0000       -32.0000       WCFTDT
       6   17400.00000   435.00000     101.31469      629.0000          .0000      LOGSALR
       7   17481.00000   437.02500      57.28762      625.0000       341.0000      LOGASST
       8    7241.00000   181.02500     194.75408     1298.0000        29.0000       CURRAT
       9    4761.00000   119.02500     203.46316     1298.0000        14.0000      QUIKRAT
      10    1336.00000    33.40000      19.63879       94.0000          .0000      NFATAST
      11    1062.00000    26.55000      17.27597       74.0000          .0000      INVTAST
      12    2087.00000    52.17500      27.45522      110.0000          .0000       FATTOT
      13    1283.00000    32.07500      31.34865      183.0000          .0000       PAYOUT
      14    1029.00000    25.72500      31.16045      147.0000       -58.0000       WCFTCL
       2     573.00000    14.32500      13.47816       57.0000       -18.0000       RETCAO

Total correlation matrix, R (i , j)

1 Analysis 1

Standard regression dependent variable is V2 RETCAP

The partial correlation matrix
Variables held constant
  4 6

Partial

IDAMS reports analysis specifications:
   Number of variable= 13
   Number of cases= 40

The most striking feature of the analysis is the extremely low value of the determinant of the correlation matrix: .79478E-0.5, which is almost close to zero. This implies multicollinearity.

Covariance ratio of a variable is the square of multiple correlation coefficient, R², with other p-1 predictor variables in the equation. It is a measure of intercorrelation. Variables, which contribute to multicollinearity can be identified from the values of Covariance Ratio.

Covariance ratios of several predictor variables are particularly high:

LOGSALE:  0.8927
LOGASST:  0.8120
CURRAT:     0.9957
NFATAST:   0.8206
INVTAST:    0.8676

The standard error of the dependent variable (7.371) is about one half of the mean, implying that the reliability of prediction by the multiple regression model. is poor.

The regression model explains 70% of the adjusted variance of the dependant variable.

As we shall see in example EX5(2), regression model with just three variables in the equation explains 80% of the adjusted variance in the dependent variable.

The F ratio of the full-scale model, though statistically significant, is much less that for the reduced model (See Example:{EX5 (2) }.

In view of high multicollinerity, there is hardly any point in interpreting the statistical significance of individual predictors.

Research Question

:

What are the factors that influence the economic performance of a company?

Economic performance is measured by the return on capital employed

Methodology

:

Stepwise Multiple Regression Analysis

Dataset

:

After filtering 40 cases read from the input data file

1
Number of variables = 13

       Number of cases = 40

       General statistics

  Variable                          Standard                            Range
    Number        Sum          Average       Deviation       Max           Min          Variable name


      3         6.51000        .16275         .29387          .6300        -1.2800        WCFTCl
      4         5.50000        .13750         .26862          .6000        -1.2800        WCFTDT
      5       186.62000       4.66550         .56091         5.7600         3.8500        LOGSALE
      6       178.48000       4.46200         .54956         5.7800         3.5400        LOGASST
      7        12.18000        .30450         .29506         1.7800          .0000        GEARRAT
      8        72.61000       1.81525         .96339         5.4400          .3600        CAPINT
      9        12.48000        .31200         .16801          .7200          .0400        NFATAST
     10        18.64000        .46600         .24250         1.1600          .0700        FATTOT
     11        10.31000        .25775         .12751          .5000          .0000        INVTAST
     12        20.99000        .52475         .67732         4.2100          .0000        PAYOUT
     13        32.78000        .81950         .43338         2.6300          .2400        QUIKRAT
     14        56.81000       1.42025         .57876         3.9800          .5400        CURRAT
      2         5.89000        .14725         .13832          .3800         -.5000        RETCAP

Total correlation matrix,R(i,j)

Step No. 0

Dependent variable is V 2 RETCAP

F-level to enter= 4.000

Standard error of Y = .1383

F-level to remove = 3.900

Variable numbers

3 4 5 6 7 8 9 10 11 12 13 14 2
**************** Listing of marginal R-squares for all potential predictors ***

Step No 1

Variable entered 4 WCFTDT

F-level 97.610

T-level 9.880

Partial

**************** Listing of marginal R-squares for all potential predictors ***

Step No 2

Variable entered 9 NFATAST

F-level 11.513

T-level 3.393

Partial

**************** Listing of marginal R-squares for all potential predictors ***

Step no 3

Variable entered 14 CURRAT

F-level 6.367

T-level 2.523

Partial

**************** Listing of marginal R-squares for all potential predictors ***

Completed 3 steps of regression

IDAMS reports analysis specifications:

Number of variables = 13
Number of cases = 40

• General Statistics

  Descriptive statistics of all predictor variables

Correlation matrix of predictor + dependent variables

Step No. 0

No variables in the model. Correlation matrix shows that V₄ (WCFTDT) has the highest correlation with the dependent variable (0.8480); Marginal RSQD (0.7198)

Hence V₄ is entered at Step 1.

Step No. 1

Variable V₄ is entered at this step with F ratio = 97.610>>FIN RATIO

With V₄ in the equation, V₉ (NFATST) is now the best candidate, since it has the highest value of RSQD.

Step No. 2

Variable V₉ is entered into the model, with F ratio = 11.513

With V₄ and V₉ in the equation, the best candidate is now V₁₄ (CURRAT) since it has the highest value of Marginal RSQD after V₄ and V₉.

Step No. 3

V14 is entered into the equation at this step. With V4 and V9 already in the equation, V14 enters with F ratio = 6.367

After this step no other variable qualifies for entering into the regression equation.

The regression model is:
RETCAP = .23146+.5048 WCFTDT-.2805 NFATAST-.0465 CURRAT

Adequacy of the fitted model

F ratio = 54.080 df (3,36) p < .000 highly significant

Standard error of the estimate of the dependent variable = .06135 which is quite low Þ high reliability of

estimation.

Determinant of the correlation matrix = .77647,

Value close to 0 Þ Multicolinearity
                       1 Þ No multicolliearity

Recall that for the full scale model the determinants of the correlation matrix was .79478E-05, which is close to 0 Þ high multicollinearity.

The standard error of the estimate is now much less than that for the full - scale model:

Full Scale Model: 7.371
Reduced Model : 0.06135

Research Question

:

What is the influence of institutional setting and rank of academic

scientists on percentage of work time devoted to teaching?

Methodology

:

Multiple Classification Analysis

Dataset

:

After filtering 1055 cases read from the input data file
3 cases contained illegal characters and were treated according to BADDATA specification
1Analysis - 1 TIME SPENT ON TEACHING

Dependent variable

1 Weighted frequency table # 1
Column var    14 : sv:inst type
Row var           9 : v204:rank
Code 1             2      3      4

1Results based on test 2 Iteration 3

Dependent variable statistics

Dependent variable (y) = 2: v262:teaching
M e a n = 41.935450
Standard deviation = 18.106530
Sum of Y = 43529.000
Sum of Y square = 2165385.0
Total sum of squares = 339976.70
Explained sum of square = 72102.410
Residual sum of squares = 267874.30
Number of cases = 1038
1 Predictor summary statistics

Predictor 9: v204:rank

Unadjusted

Eta-square = .10896630      Beta-square = .53927850E-01

Eta = .33010040        Beta = .23222370

Eta-square(adj)= .10724440

Eta(adj)= .32748200

Unadjusted deviation SS = 37045.990
Adjusted deviation SS = 18334.210

Predictor 14: sv:inst type

Unadjusted

Eta-square = .16380060 Beta-square = .11275420

Eta = .40472280       Beta = .33578890

Eta-square(adj)= .16137450

Eta(adj)= .40171440

Unadjusted deviation SS = 55688.370

Adjusted deviation SS = 38333.800

1 Analysis summary statistics

R-squared (unadjusted) = proportion of variation explained by fitted model = .21208
Adjustment for degrees of freedom = 1.00484

***Multiple R (adjusted) = .45636       Multiple R-squared (adjusted) = .20826
1Dependent variable       2: v262:teaching

Listing of Betas in descending order

***Multiple R (adjusted) = .45636 Multiple R-squared (adjusted) = .20826

IDAMS reports analysis specifications:

Number of cases read= 1055 cases
Number of cases eliminated due to bad data/missing values
in the dependent variables =17.
Number of cases processed= 1038

a = Parameters for convergence

Variables:

Bivariate frequency table
V14 (rows) ´ V9 (columns)
Type of Institutions ´ Rank

Dependent variable statistics
(A)   Grand mean : 41..935450
         Standard Deviation: 18..106530

Predictor Summary Statistics
First predictor V9 : Rank
(B)  Class mean = Average time spent by the academic scientist of a given category

Deviation from the grand mean = Class mean – Grand mean

Coefficient = Deviation of the class mean from the grand mean after holding constant the other predictors (in this case V14 )

Adjusted mean = Grand mean + Coefficient

(a) Grand mean = 41.935450
V9(Class 1) – (Prof.)
(b) Class mean = 34.8237
(c) Deviation = (b)-(a) = -7.117600
(d) Coefficient = -4.985940
(e) Adjusted mean = (a)+(d) = 41.935450 + (-) 4.985940 = 36.94951

Eta square = .10896630
Eta square indicates that approximately 11 per cent of the variance in the dependent variable (i.e. time spent on teaching) is explained by V9 (rank)

Eta square is an approximate measure of the relationship between V9 (rank) and V2 (percentage of time spent on teaching)

Eta square adjusted = .10724440
Eta square adjusted indicates that approximately 10.7% of the variance in the dependent variable (V2) is explained by V9, while holding constant the other predictor.

Unadjusted deviation sum of squares = Sum of squares for the predictor based on unadjusted deviations from grand mean.

Adjusted deviations sum of squares = As above but based on adjusted deviations of the predictor from the grand mean.

Summary Statistics

R² unadjusted indicates that approximately 21% of the variance in the dependent variable is explained by the fitted model.
Adjustment for degrees of freedom = 1.00484
R² adjusted = R² unadjusted / adjustment = .20826

There is not much difference between the values of the unadjusted and adjusted R², which implies that there is hardly any interaction between the two variable categories.

The predictors are ranked by Beta values, which show relative importance of the two predictors.

Institutional setting of an academic scientist seems to have greater effect on the time spent by an academic scientist than his rank.

1 Analysis - 2 TIME SPENT ON TEACHING

Dependent variable statistics

Dependent variable (y) = 2: v262:teaching
M e a n = 40.723580
Standard deviation = 15.807100
Sum of Y = 40072.000
Sum of Y square = 1877492.0
Total sum of squares = 245616.80
Explained sum of square = 51493.110
Residual sum of squares = 194123.70
Number of cases = 984

1 Predictor summary statistics

Predictor 9: v204:rank

Unadjusted

Eta-square = .11281920   Beta-square = .62690240E-01

Eta = .33588570    Beta = .25038020

Eta-square(adj)= .11101050

Eta(adj)= .33318240

Unadjusted deviation SS = 27710.290
  Adjusted deviation SS = 15397.780

Predictor 14: sv:inst type

Unadjusted

Eta-square = .15333510   Beta-square = .10420150

Eta = .39158030   Beta = .32280260

Eta-square(adj)= .15074330

Eta(adj)= .38825680

Unadjusted deviation SS = 37661.680
Adjusted deviation SS = 25593.650

1 Analysis summary statistics
R-squared (unadjusted) = proportion of variation explained by fitted model = .20965
Adjustment for degrees of freedom = 1.00511

***Multiple R (adjusted) = .45344 Multiple R-squared (adjusted) = .20561
1 Dependent variable     2: v262:teaching

Listing of Betas in descending order

***Multiple R (adjusted) = .45344 Multiple R-squared (adjusted) = .20561

In this analysis outlier cases have been eliminated.
IDAMS reports analysis specifications:

Number of cases read = 1055 cases.
Number of cases eliminated due to bad data/missing values= 17
Number of cases eliminated due to outliers 54
Total number of cases eliminated= 71
Number of cases processed= 984

a ‘Parameters’, for convergence

Dependent variable statistics
(C)      Grand mean : 40.723580
           Standard Deviation: 15.807100

Predictor Summary Statistics
First predictor V9 : Rank
(D)     Class mean = 34.4375 ( Average time spent by the academic scientist of a given category)
Deviation from the grand mean = Class mean – Grand mean

Coefficient = Deviation of the class mean from the grand mean after holding constant the other predictors (in this case V14 )

Adjusted mean = Grand mean + Coefficient

(a)Grand mean = 40.723580
V9(Class 1) – (Prof.)
(b) Class mean = 34. 4375
(c) Deviation = (b)-(a) = -6.2860760
(d) Coefficient = -4.985940
(e) Adjusted mean = (a)+(d) = 40.723580+(-)4.985940 = 36.031230

Eta square = .11281920
Eta square indicates that approximately 11.3 per cent of the variance in the dependent variable (i.e. time spent on teaching) is explained by V9 (rank)

Eta square is an approximate measure of the relationship between V9 (rank) and V2 (percentage spent on teaching)

Eta square adjusted = .11101050
Eta square adjusted indicates that approximately 11.1% of the variance in the dependent variable (V2) is explained by V9, while holding constant other predictors.

Unadjusted deviation sum of squares = Sum of squares for the predictor based on unadjusted deviations from the grand mean.

Adjusted deviations sum of squares = As above, but based on adjusted deviations of the predictor from the grand mean.

Summary Statistics
R² unadjusted indicates that approximately 21% of the variance in the dependent variable is explained by the fitted model.
Adjustment for degrees of freedom = 1.00511
R² adjusted = R² unadjusted / adjustment = .20965

There is not much difference between the values of the unadjusted and adjusted R² which implies that there is hardly any interaction between the two variable categories.

The predictors are ranked by Beta values, which show relative importance of the two predictors.

Institutional setting of an academic scientist seems to have greater effect on the time spent by an academic scientist than his rank.