quantitive techniques in business

Quantitive Techniques in Business

Final projectQuantitive Techniques in BusinessA report Submitted to The Department of Management and Administrative Sciences, University of Gujrat in Partial Fulfillment of the Requirements For the Degree of Master in Business Administration

Submitted By:Muhammad Jahanzaib (11022720-028)MBA 4th (3.5Year) Session (2011-2015)

Name of Program Coordinator: Mr. Mirza Rizwan Sajid

UNIVERSITY OF GUJRAT Date of Submission 27/06/2014

Table of ContentS. NoDescription

1Introduction

2Type of analysis

3Univariate test

4Bivariate test

5Association test

6Correlation test

7Regression Analysis

8Simple regression model

9Multiple regression model

10Assumption of regression model

11Normality

12Linearity

13Homocedascity

14Autocorrelation

15Multicolinerity

16Means compare test

17Parameter test

18Simple t test

19Independence t test

20Compare t test

21ANOVA

22Non parameter test

23Factor Analysis

24Explanatory Factor Analysis

25Confirmatory Factor Analysis

Introduction

The project is about the application of the tools and techniques studied in the subject quantitative technique in business. During my semester, I have studied number of techniques and their practical application in the software. I have applied all the tools and techniques studied in this course using SPSS. This work proves very helpful in research work as well as for data analysis. In this project, I used 5 variables out of which 2 variables were qualitative (Nominal) and remaining 3 were quantitative variables. Tools and techniques which are practiced in this project include: univariate Analysis, Bivariate Analysis, Multivariate analysis, histogram, pie charts, bar chart, regression analysis including simple regression and multiple regression models, parametric and non-parametric tests, mean comparison and factor analysis with interpretation.

Types of analysis

There are three types of analysis:

Univariate Analysis Bivariate Analysis Multivariate Analysis

Univariate Analysis

Quantitative variables

My quantitative variables include

Serial NoVariables

1Debt ratio

2Bankruptcy Risk

3Liquidity Risk

1. Debt RatioDescriptive Statistics

NMinimumMaximumMeanStd. Deviation

Debts Ratio50.211.09.5332.20868

Valid N (list wise)50

Histogram

Interpretation:The Debt ratio is Quantitative variable and for quantitative variables we make histogram. According to results the average Debt Ratio of the respondents is 0.5332 and minimum value is 0.21 and maximum value is 1.09. While standard deviation is 0.20868, Subject vise interpretationOn the basis of given sample information we can conclude that firm average debt use more than 50% of its capital and minimum debt are use 0.21 and some firm use debt more than of its whole equity.

2. Bankruptcy RiskDescriptive Statistics


Bankruptcy Risk503.356.765.1300.85697


Histogram

Interpretation:

The Bankruptcy risk is Quantitative variable and for quantitative variables we make histogram. According to results the average value is 5.13. Minimum value is 3.35 and maximum value is 6.76, while standard deviation is 0.8569.Subject vise interpretationOn the basis of given sample information we can conclude that firms are bear bankruptcy risk average 5.13 that result show the all the firms must face liquidity risk.

3. Liquidity Risk Descriptive Statistics


Liquidity Risk50.303.481.5554.81707


Histogram

Interpretation:The Liquidity risk is Quantitative variable and for quantitative variables we make histogram. According to results the average value is 1.5554, and Minimum value is 0.30 and maximum value is 3.48, and the standard deviation is 0.81707.

Subject vise interpretationOn the basis of given sample information we can conclude that firm are average liquidity is 1.55 firms must maintain liquidity close to 1 because firm are liabilities are easily pay at any time.

Qualitative Variables

Followings are my qualitative variables:

Serial NoVariables

1Debt Strategies

2 Profit Loss

1. Debt Strategies

Firms are debts strategies implement/ Non implement

FrequencyPercentValid PercentCumulative Percent

ValidImplement2550.050.050.0

non implement2550.050.0100.0

Total50100.0100.0

Bar chat

Interpretation:The Debt strategies are qualitative variable and in case of qualitative variable we make bar chart or pie chart. According to given results out of 50 respondents 50% of the respondents are implement the debt strategies on firms and 50% of respondents are not implement the debt strategies on firms.

Subject vise interpretationOn the basis of given sample information we can conclude that half firms uses debt strategies and half firms use not implement the debt strategies.

2. Profit & Loss

Company Earn profit Or suffering Loss

FrequencyPercentValid PercentCumulative Percent

Validprofit2856.056.056.0

Loss2244.044.0100.0

Total50100.0100.0

Interpretation:This is qualitative variable and in case of qualitative variable we make bar chart or pie chart. According to our results 44% respondents have their bearing loss and remaining 56% of respondents enjoying a profit.

Subject vise interpretationOn the basis of given sample information we can conclude that 44 percent firms suffering losses and 56 percent earn profit.

Bivariate Analysis

Quantitative Variables

1. Debt Ratio & Bankruptcy Risk2. Debt Ratio & Liquidity Risk

Debt Ratio

One-Sample Kolmogorov-Smirnov Test

Debts_Ratio

N50

Normal ParametersaMean.5332

Std. Deviation.20868

Most Extreme DifferencesAbsolute.103

Positive.103

Negative-.088

Kolmogorov-Smirnov Z.730

Asymp. Sig. (2-tailed).661

a. Test distribution is Normal.

Interpretation

1. Hypothesis Formulation Ho: Data is Normal.H1: Data is not normal.2. Level of Significance: = 0.053. Test-statistic: One sample t-test4. Critical Region: p > 5. Calculations: p = 0.6616. Conclusion: To check the normality assumption we applied KS Test. Since P-Value is 0.661 which is Greater than 0.05. So we will reject our Alternative hypothesis. So our data is normal.

Bankruptcy Risk


Bankruptcy_Risk

N50

Normal ParametersaMean5.1300



Positive.070

Negative-.139




Interpretation


Association test

firms are debts strategies implement/ Non implement * company Earn profit Or suffering Loss Cross tabulation

Count company Earn profit or LossTotal

ProfitLoss

firms are debts strategies implement/ Non implementimplement18725

non implement101525

Total282250

Interpretation1. There is generating hypothesis: H0: There is no association between debts strategies and profit. H1: There is association between debts strategies and profits.2. Level of Significance: = 0.053. Test-statistic: Chi-square test4. Critical Region: p < 5. Calculations: p = 0.023 and chi square = 5.1956. Conclusion: On the basis of given sample information we conclude that there is an association between debt strategies and profit. These firms are implement the debt strategies are earn profit or good performed, but on the other hand these firms are not implement strategies that are more chance to suffering loss or low performed in market.

Subject vise interpretationOn the basis of given sample information we can conclude that association between that firms use dept strategies are earn profit and that are not apply these are suffering loss.

Correlation

Correlations

Debts RatioBankruptcy Risk

Spearman's rhoDebts RatioCorrelation Coefficient1.000.506**

Sig. (2-tailed)..000

N5050

Bankruptcy RiskCorrelation Coefficient.506**1.000

Sig. (2-tailed).000.

N5050

**. Correlation is significant at the 0.01 level (2-tailed).

Interpretation1. There is generating hypothesis: H0: There is no correlation between Debt ratio and bankruptcy risk. H1: There is correlation between Debt ratio and bankruptcy risk.2. Level of Significance: = 0.053. Test-statistic: Chi-square test4. Critical Region: p < 5. Calculations: p = 0.000 and Pearson Test = 0.5376. Conclusion: Data is normal distribution thus used the Pearson Test of correlation the Probability of significance is 0.000 less than selected P-.value thus null hypothesis is rejected. On the basis of given sample information we conclude that there is a highly strong correlation between debt Ratio and bankruptcy Risk.

Subject vise interpretationOn the basis of given sample information we can conclude that result shows that if the bankruptcy risk increase debt ratio also increases if bankruptcy risk decrease debt ratio also decrease there is highly strong positive relationship between bankruptcy risk and debt ratio.

Regression Model

1. Simple Linear Regression2. Multiple Linear Regression

Simple Linear Regression

Model Summary

ModelRR SquareAdjusted R SquareStd. Error of the Estimate

1.537a.289.274.17783

a. Predictors: (Constant), Bankruptcy Risk

Interpretation:According to model summary results of simple linear regression model shows that R-square value is 0.289 which is less significant. This value says that the simple regression (Bankruptcy risk) explains only 28.9% of the variation in dependent variable (Debt Ratio).

1. Hypothesis Formulation:Ho: Model is not fit for prediction. H1: Model is fit for prediction.2. Level of Significance: = 0.053. Test-statistic: ANOVA4. Critical Region: p < 5. Calculations: p = 0.000

ANOVAb

ModelSum of SquaresdfMean SquareFSig.

1Regression.6161.61619.477.000a

Residual1.51848.032

Total2.13449

a. Predictors: (Constant), Bankruptcy Risk

b. Dependent Variable: Debts Ratio

Conclusion: According to given results we in a position to reject Ho. So we have to accept Alternative Hypothesis that model is fit for perdition

Coefficients

ModelUnstandardized CoefficientsStandardized CoefficientsTSig.

BStd. ErrorBeta

1(Constant).138.154-.895.375

Bankruptcy Risk.131.030.5374.413.000

a. Dependent Variable: Debts Ratio

Interpretation:According to our table the values: = 0.1381 = 0.131So Our Simple linear equation: Y = (0.138) + (0.131) X Subject vise interpretationOn the basis of given sample information we can conclude that independent variable is more effect to dependent variable if bankruptcy risk is increase than also increase debt ratio. If bankruptcy risk decrease than debt ratio also decreased.

Multiple Linear Regression Model

Regression Model:Debts Ratio = + 1 (Bankruptcy Risk) + 2 (Liquidity Risk)

Model Summary

ModelRR SquareAdjusted R SquareStd. Error of the Estimate

1.627a.393.367.16598

a. Predictors: (Constant), Liquidity Risk, Bankruptcy Risk

Interpretation:According to model summary results of multiple linear regression model shows that R-square value is 0.393 which is significant. This value says that in the multiple regressions model (independent variables) explains 39.3% of the variation in dependent variable (Debt ratio).

1. Hypothesis Formulation:Ho: Model is not fit for prediction. H1: Model is fit for prediction.2. Level of Significance: = 0.053. Test-statistic: ANOVA4. Critical Region: p < 5. Calculations: p = 0.000

ANOVAb


1Regression.8392.41915.227.000a

Residual1.29547.028

Total2.13449



6. Conclusion: According to given results we are in a position to reject Ho. And alternative hypothesis accepts so we have to accept that model is fit for perdition.

Coefficients

ModelUnstandardized CoefficientsStandardized CoefficientstSig.

BStd. ErrorBeta

1(Constant).229.1931.187.241

Bankruptcy Risk.088.032.3602.782.008

Liquidity Risk-.094.033-.369-2.846.007


Interpretation:According to our table the values:

= .2201 = 0.0882 = -.094

Debts Ratio = + 1 (Bankruptcy Risk) + 2 (Liquidity Risk)

Debts Ratio = .229 + .088 (Bankruptcy Risk) + -0.94 (Liquidity Risk)

Subject vise interpretationOn the basis of given sample information we can conclude that both independent variables are effect to dependent variable if bankruptcy risk and liquidity risk increase debt ratio increase if decrease debt ratio decrease.

Assumptions of linear regression

1. Normality:


Debts_Ratio

N50

Normal ParametersMean.5332



Positive.103

Negative-.088




Interpretation


Histogram

Interpretation:It is also clear from the histogram that data is not normal. For showing normality it should be of bell shaped. This is more on the left side. This histogram is positively skewed.

P.P Plot for Saving (Dependent Variable)

Interpretation:The results in p-p plot shows that data is not normal.

2. Linearity

Scatter DiagramDiagram of Debt ratio, Bankruptcy risk and liquidity risk

Interpretation:We can see from the scatter diagram that no variable is linear. The relationship between Debt ratio and Bankruptcy risk is not leaner and relationship between Debt ratio and Liquidity risk is almost leaner.

Scatter DiagramDiagram of debt ratio, debt strategies and profit & loss

Interpretation:We can see from the scatter diagram that no variable is linear. The relationship between Debt ratio and Debt strategies is not leaner and relationship between Debt ratio and Profit &Loss is not leaner.

3. Homocedascity

Independent Samples Test

Levines Test for Equality of Variancest-test for Equality of Means

FSig.tdfSig. (2-tailed)

Debts RatioEqual variances assumed2.456.1242.09648.041

Equal variances not assumed2.16847.934.035

Bankruptcy RiskEqual variances assumed.189.6662.69548.010

Equal variances not assumed2.73347.203.009

Liquidity RiskEqual variances assumed3.325.074-1.82048.075

Equal variances not assumed-1.75837.888.087

Interpretation:

On the basis of given sample information to conclude that we are apply a Levines test for Equality of variances all the variables significance level set 0.05, but our results are debt ratio is 0.124, bankruptcy risk is 0.666 and liquidity risk is 0.074 which is all p values are insignificance. Thus to conclude that in our sample data are not homocedascity that is hetrocedascity.

4. Auto Correlation

Model Summaryb

ModelRR SquareAdjusted R SquareStd. Error of the EstimateDurbin-Watson

1.627a.393.367.165980.917

a. Predictors: (Constant), Liquidity Risk, Bankruptcy Riskb. Dependent Variable: Debts Ratio

InterpretationApplying the independence test the value of Durbin-Watson is 0.917 thus in variables problem of auto correlation occurred. This value is not lying between 1.5 -- 2.5. So there is serious effect of auto-correlation.

ANOVAs


1Regression.8392.41915.227.000a

Residual1.29547.028

Total2.13449



5. No Multicorenarity

Coefficients

ModelUnstandardized CoefficientsStandardized CoefficientstSig.Collinearity Statistics

BStd. ErrorBetaToleranceVIF

1(Constant).229.1931.187.241

Bankruptcy Risk.088.032.3602.782.008.7701.299E0

Liquidity Risk-.094.033-.369-2.846.007.7701.299E0


Interpretation

In the coefficient table we have to check the tolerance and VIF under colinearity Statistics. Here the T value should be greater than 0.2 and VIF values less than 5 are considered favorable. In table we can see that T value of all variables is more than 0.2 more over VIF value is less than 5 which are favorable values.

Collinearity Diagnosticsa

ModelDimensionEigenvalueCondition IndexVariance Proportions

(Constant)Bankruptcy RiskLiquidity Risk

112.8101.000.00.00.02

2.1813.936.01.03.60

3.00918.122.99.97.38


InterpretationIn collinearity diagnostics the condition index values less than 30 shows no big issue of multicollinarity. In our results the value condition index 18.122 thus there is no multicollonarity in our debt.

Mean Comparison

S. NoParametric TestsNon-Parametric Tests

1One Sample T-TestSign test

2Independent Sample test Independent sample /Mann Whitney U-test

3Paired Sample test Wilcoxen Sign rank test

4ANOVA Kruskal- wallindependent test

Parametric Test

1. One Sample T-Test

Debt Ratio

For the application of parametric tests I am supposing that the variable Debt ratio have normal data. 1. Hypothesis Ho: Average Debt ratio =0.50H1: Average Debt ratio 0.502. Level of Significance: = 0.053. Test-statistic: One sample t-test4. Critical Region: p < 5. Calculations: p = 0.000

One-Sample Statistics

NMeanStd. DeviationStd. Error Mean

Debts Ratio50.5332.20868.02951

One-Sample Test

Test Value = 0

TDfSig. (2-tailed)Mean Difference95% Confidence Interval of the Difference

LowerUpper

Debts_Ratio18.06649.000.53316.4739.5925

6. Conclusion: On the basis of given data we are not in a position to accept Ho. Since P-Value is 0.000 which is less than 0.05. So we will reject our null hypothesis. So average family saving is Average Debt ratio 0.50

2. Independent Sample Test

1. Hypothesis Ho: Data is Normal.H1: Data is not normal. 2. Level of Significance: = 0.053. Test-statistic: One sample t-test 4. Critical Region: p < 5. Calculations: p = 0.124 & p = 0.196


GroupCGPA

MaleN30




Positive.165

Negative-.271

Kolmogorov-Smirnov Z1.485


MaleN20




Positive.241

Negative-.223




6. Conclusion: On the basis of given data we are not in a position to reject Null Hypothesis Since P-Value is 0.124 and 0.196 which is more than 0.05. So we will reject our null hypothesis. So our data is normal

1. Hypothesis Ho: Ho= f = mH1: Ho= f m2. Level of Significance: = 0.053. Test-statistic: Independent Sample Test4. Critical Region: p < 5. Calculations: p = 0.00022Group Statistics

GroupNMeanStd. DeviationStd. Error Mean

CGPAmale303.1357.14738.02691

Male203.5840.23266.05202

Independent Samples Test

Levene's Test for Equality of Variancest-test for Equality of Means

FSig.tdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the Difference

Lower

CGPAEqual variances assumed1.595E1.00022 -8.3553748.000-4.48333E-15.36581E-2-.55622

Equal variances not assumed-7.654492.916E1.000-4.48333E-15.85713E-2-.56810

6. Conclusion:On the basis of given sample we are rejected to Ho. Since P-Value is 0.00022 which is less Than 0.05 so we can say that CGPA Male and females are not same.

3 Paired Sample Test1. Hypothesis Ho: Data is Normal.H1: Data is not normal. 2. Level of Significance: = 0.053. Test-statistic: One sample t-test 4. Critical Region: p < 5. Calculations: p = .039


difference

N50

Normal ParametersaMean.1098



Positive.199

Negative-.141




6. Conclusion: According to results we are rejected to H0. So our Data is not normal. But we assume data are normal for checking the parametric test (paired sample test).

Paired sample test Hypothesis Ho: Ho= B = A (CGPA before and CGPA are equal after gaudiness)H1: H1= B E (CGPA before and CGPA are not equal after gaudiness)Level of Significance: = 0.05Test-statistic: Paired Sample StatisticsCritical Region: p < Calculations: p = 0.001

Paired Samples Statistics

MeanNStd. DeviationStd. Error Mean

Pair 1CGPA3.315050.28822.04076

After CGPA3.424850.29287.04142

Paired Samples Test

Paired DifferencestdfSig. (2-tailed)

MeanStd. DeviationStd. Error Mean95% Confidence Interval of the Difference

LowerUpper

Pair 1CGPA After CGPA-1.09800E-1.20903.02956-.16920-.05040-3.714E049.001

6. Conclusion:According to results the p-value is less alpha value. So we are rejected to H0 and we have to accept Null hypothesis CGPA before and after gaudiness are not equal. ANOVA1. Hypothesis Ho: Data is Normal.H1: Data is not normal. 2. Level of Significance: = 0.053. Test-statistic: One sample t-test 4. Critical Region: p < 5. Calculations: p = .019 & .109 & .220


Group_AnovaCGPA

Lower familyN16




Positive.191

Negative-.381



Middle FamilyN18




Positive.284

Negative-.218



Upper FamilyN15




Positive.254

Negative-.271




6. Conclusion:According to results only business man variable data is not normal. We supposed that our data is Normal. So now we apply ANOVA Test on it

ANOVA:1. Hypothesis Ho: Ho= S = B = E (CGPA of lower class student, middle and upper is Equal)H1: H1= S B E(CGPA of lower class student, middle and upper is not equal) 2. Level of Significance: = 0.053. Test-statistic: One Way ANOVA4. Critical Region: p < 5. Calculations: p = 0.000

ANOVA

CGPA

Sum of SquaresdfMean SquareFSig.

Between Groups2.41212.41269.812.000

Within Groups1.65848.035

Total4.07049

6. Conclusion: On the basis of given data we are no rejected Ho. Since P-Value is 0.000 which is less than 0.05. So we can say that CGPA of lower class student, middle and upper are not equal.

Non-Parametric Tests

Mann-Whitney Test1. Hypothesis Ho: Ho= m = f (CGPA of male and female are equal)H1: H1= m f (CGPA of male and female are not equal)2. Level of Significance: = 0.053. Test-statistic: Mann-Whitney Test4. Critical Region: p < 5. Calculations: p = 0.000

Ranks

GroupNMean RankSum of Ranks

CGPAMale3015.50465.00

Male2040.50810.00

Total50

Test Statistics

CGPA

Mann-Whitney U.000

Wilcoxon W465.000

Z-5.995


a. Grouping Variable: Group

6. Conclusion: According to the results the P-value is less than the alpha value and on the basis of this p-value we are rejected the null hypothesis. So we have to accept that CGPA of male and females are not equal.

Wilcoxon Signed Ranks Test1. Hypothesis Ho: Ho= B = A (Saving before and saving are equal after increase in salary)H1: H1= B A (Saving before and saving are not equal after increase in salary)2. Level of Significance: = 0.053. Test-statistic: Wilcoxon Signed Ranks Test4. Critical Region p < 5. Calculations: p = 0.00

Ranks

NMean RankSum of Ranks

Group CGPANegative Ranks50a25.501275.00

Positive Ranks0b.00.00

Ties0c

Total50

a. Group < CGPA

b. Group > CGPA

c. Group = CGPA

Test Statistics

Group CGPA

Z-6.170a


a. Based on positive ranks.

b. Wilcoxon Signed Ranks Test

6. Conclusion:As per the given data the results shows that the p-value is less than alpha value which is 0.000 < 0.05. So we are not in a position to accept Ho. So we have to accept that CGPA before and after Gaudiness not equal.

FACTOR ANALYSIS

1. Explanatory Factor Analysis2. Confirmatory Factor Analysis

Explanatory Factor Analysis

1. Hypothesis Ho: Ho= Data is suitable for Factor Analysis. H1: H1= Data is not suitable for Factor Analysis.2. Level of Significance: = 0.053. Test-statistic: KMO and Bartlett's Test4. Critical Region: p < 5. Calculations: p = 0.00

KMO and Bartlett's Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy..693

Bartlett's Test of SphericityApprox. Chi-Square35.911

df3

Sig..000

6. Conclusion:According to the KMO value given in results 0.0.693 we can say that sample is 69.3% that is Almost sufficient that is close to 70%. On the basis of given data we can say that p-value is less than alpha value so null hypothesis is rejected. So our data is not suitable for factor analysis.

Communalities

InitialExtraction

Debts Ratio1.000.714

Bankruptcy Risk1.000.661

Liquidity Risk1.000.665

Extraction Method: Principal Component Analysis.

Interpretation:As per the given data the initial values of all the variables are 1 showing that each variable is playing 100% role. But in extraction, the values greater than 0.6 are favorable. Variables having extraction values above 60% are favorable in extracting information and these variables are playing important role in factor analysis.

Total Variance Explained

ComponentInitial EigenvaluesExtraction Sums of Squared Loadings

Total% of VarianceCumulative %Total% of VarianceCumulative %

12.04067.98867.9882.04067.98867.988

2.52017.33785.326

3.44014.674100.000


InterpretationOn the basis of given data one variable have total value more than 1 so these variables should be included into the factor. This variable explains 67.98% variation. So we have to accept this variable for factor analysis.

Interpretation

The Screen Plot shows that all the points above 1 should be included into factor. There is one point above 1.

Component Matrix

Component

1

Debts Ratio.845

Bankruptcy Risk.813

Liquidity Risk-.815


a. 1 component extracted.

InterpretationOn the basis of given sample information only one variable have been generated, this is given below:Factor 1: Debt ratio, Bankruptcy risk and liquidity risk.

Rotation competent Matrix Only one component extracted thus the solution are not generated.

Muhammad Jahanziab11022720-028Page 37

quantitive techniques in business

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