# Correlation Analysis Between Dependent And Independent Variables Finance Essay

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This chapter discusses on the results and analysis of this study based on the data collection from seventy Iranian firms in order to investigate the research hypotheses of this survey. The first section of this chapter investigates the demographic variables using descriptive statistics. This part then used descriptive analysis to summarize the research variables including dependent and independent variables. The chapter then proceeds with a discussion on regression analysis in order to fulfill the research hypotheses. The chapter finally ends with a correlation analysis between dependent and independent variables. In order to perform statistical analysis, the SPSS version 16 was used.

## Systematic Risk

The Table 4-1 summarized the descriptive statistics for systematic risk. According to Table 4-1, the mean and standard deviation for systematic risk are 1.1803 and 1.462.

Table 4: Descriptive Statistics for Systematic Risk

N

Minimum

Maximum

Mean

Std. Deviation

Systematic Risk

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70

-.34

8.75

1.1803

1.46278

Valid N (listwise)

70

## Account Profit Beta

The Table 4-2 summarized the descriptive statistics for Accounting Profit Beta. According to Table 4-2, the mean and standard deviation for Accounting Profit Beta are 0.4378 and 0.31267.

Table 4: Descriptive Statistics for Account Profit Beta

N

Minimum

Maximum

Mean

Std. Deviation

Account Profit Beta

70

-.41

.94

.4378

.31267

Valid N (listwise)

70

## Cash Flow Beta

The Table 4-3 summarized the descriptive statistics for Cash Flow Beta. According to Table 4-3, the mean and standard deviation for Cash Flow Beta are 0.3267 and 0.31233.

Table 4: Descriptive Statistics for Cash Flow Beta

N

Minimum

Maximum

Mean

Std. Deviation

Cash Flow Beta

70

-.50

1.00

.3267

.31233

Valid N (listwise)

70

## Networking Capital

The Table 4-4 summarized the descriptive statistics for Networking Capital. According to Table 4-4, the mean and standard deviation for Networking Capital are 2.7233 and 1.34830E7.

Table 4: Descriptive Statistics for Networking Capital

N

Minimum

Maximum

Mean

Std. Deviation

NWC

70

15691.78

88133556.00

2.7233E6

1.34830E7

Valid N (listwise)

70

## Statistics for Assets

The Table 4-5 summarized the descriptive statistics for Assets. According to Table 4-5, the mean and standard deviation for Assets are 1.6858E6 and 5.23948E6.

Table 4: Descriptive Statistics for Assets

N

Minimum

Maximum

Mean

Std. Deviation

Assets

70

43541.67

39928010.00

1.6858E6

5.23948E6

Valid N (listwise)

70

## Testing Hypotheses Using Multiple Regressions

In this research study, it is assumed that there is no constant in regression equation. Hence, the constant was removed from multiple regression equation. The outputs of multiple regression modeling were represented in Table 4-7, 4-8, and 4-9. The first step to examine the multiple regressions is to test normality assumption. According to Royston (1992), for samples with sizes between 3 and 2000 the Shapiro-Wilk test is suitable examination. In order to test normality assumption, standardized residuals were used. Since, the p-value for standardized residuals equals .2 (Under Shapiro-Wilk test), which is more than 0.05 thus it can be concluded that the normality assumption was met. Hence, for these four independent variables multiple regression analysis can be done. The results were represented in Table 4-6.

Table 4: Tests of Normality

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

Standardized Residual

.172

70

.12

.776

70

.2

a. Lilliefors Significance Correction

In this study, all Assets, Networking Capital, Cash Flow Beta, Account Profit Beta were regressed on Systematic Risk. As shown in table 4-7, the R-Square of this regression model equals 0.556. The Durbin-Watson is of 1.995 drops between 1.5 and 2.5. This indicated that there is no autocorrelation problem among the error terms. Therefore, it approved that error terms were independent. According to Table 4-9, the co linearity statistics represents that tolerance statistics for Account Profit Beta, Cash Flow Beta, Networking Capital, and Assets are all greater than 0.1, and VIF (Variation Inflation Factors) for these variables are all lesser than 10. Hence, it can be stated that these variables have no multi co linearity problem. Therefore, the research hypothesis and regression analysis strongly supported.

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Table 4: Model Summary

Model

R

R Squareb

Adjusted R Square

Std. Error of the Estimate

Durbin-Watson

1

.745a

.556

.529

1.28483

1.995

a. Predictors: Assets, Networking Capital, Account Profit Beta, Cash Flow Beta

b. For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models which include an intercept.

c. Dependent Variable: Systematic Risk

d. Linear Regression through the Origin

According to Table 4-8, the ANOVA procedure provided F-value equals 20.626 (F=20.626) with p-value of 0.000 which is lesser than 0.05 (Sig=0.000<0.05). Hence, it is strongly supported that regression modeling is significant and at least one of the predictors namely Account Profit Beta, Cash Flow Beta, Networking Capital, and Assets can be used to predict Systematic Risk.

Table 4: ANOVA

Model

Sum of Squares

Df

Mean Square

F

Sig.

1

Regression

136.200

4

34.050

20.626

.000a

Residual

108.953

66

1.651

Total

245.153b

70

a. Predictors: Assets, Networking Capital, Account Profit Beta, Cash Flow Beta

b. This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.

c. Dependent Variable: Systematic Risk

d. Linear Regression through the Origin

Table 4: Coefficients

Model

Unstandardized Coefficients

Standardized Coefficients

T

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

Account Profit Beta

1.284

.413

.368

3.106

.003

.479

2.086

Cash Flow Beta

1.595

.494

.384

3.230

.002

.477

2.098

Networking Capital

-3.686E-10

.000

-.003

-.032

.974

.958

1.044

Assets

5.447E-8

.000

.159

1.897

.062

.957

1.045

a. Dependent Variable: Systematic Risk

b. Linear Regression through the Origin

The results of Table 4-9 confirmed that there were two financial ratios including Account Profit Beta and Cash Flow Beta, which positively associated with Systematic Risk. As can be seen in Table 4-9, two predictors namely Account Profit Beta (B=1.284, Sig=0.003<0.05) and Cash Flow Beta (B=1.595, Sig=0.002<0.05) were all directly contributed in predicting Systematic Risk. As shown in Table 4-9, there is no significant relationship between Networking Capital (sig=0.974>0.05) and Assets (sig=0.062>0.05) with Systematic Risk. In addition, the results also indicated that Cash Flow Beta with highest coefficient value is the most important variable to predict Systematic Risk.

In order to have a clear picture of multiple regression equation a stepwise method is recommended. The results of multiple regression using stepwise method are represented in Table 4-10, Table 4-11, and Table 4-12.

In this section, all Assets, Networking Capital, Cash Flow Beta, Account Profit Beta were regressed on Systematic Risk using stepwise regression analysis. As shown in table 4-10, the R-Square for model 2 of this regression model equals 0.531. The Durbin-Watson of 1.828 drops between 1.5 and 2.5. This indicated that there is no autocorrelation problem among the error terms. Therefore, it approved that error terms were independent. According to Table 4-12, the co linearity statistics represents that tolerance statistics for Account Profit Beta, Cash Flow Beta are all greater than 0.1, and VIF (Variation Inflation Factors) for these variables are all lesser than 10. Hence, it can be stated that these variables have no multi co linearity problem. Therefore, the research hypothesis and regression analysis strongly supported.

Table 4: Model Summary for Stepwise Regression

Model

R

R Squareb

Adjusted R Square

Std. Error of the Estimate

Durbin-Watson

1

.679a

.461

.453

1.38437

2

.729c

.531

.518

1.29988

1.828

a. Predictors: Cash Flow Beta

b. For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models, which include an intercept.

c. Predictors: Cash Flow Beta, Account Profit Beta

d. Dependent Variable: Systematic Risk

e. Linear Regression through the Origin

According to Table 4-11, under model 2, the ANOVA procedure provided F-value equals 38.544 (F=38.544) with p-value of 0.000 which is lesser than 0.05 (Sig=0.000<0.05). Hence, it is strongly supported that regression modeling is significant and at least one of the predictors namely Account Profit Beta, Cash Flow Beta, Networking Capital, and Assets can be used to predict Systematic Risk.

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Examples of our workTable 4: ANOVA for Stepwise Regression

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

112.915

1

112.915

58.918

.000a

Residual

132.238

69

1.916

Total

245.153b

70

2

Regression

130.254

2

65.127

38.544

.000c

Residual

114.899

68

1.690

Total

245.153b

70

a. Predictors: Cash Flow Beta

b. This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.

c. Predictors: Cash Flow Beta, Account Profit Beta

d. Dependent Variable: Systematic Risk

e. Linear Regression through the Origin

Table 4: Coefficient for Stepwise Regression

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

Cash Flow Beta

2.820

.367

.679

7.676

.000

1.000

1.000

2

Cash Flow Beta

1.678

.496

.404

3.383

.001

.484

2.068

Account Profit Beta

1.334

.416

.382

3.203

.002

.484

2.068

a. Dependent Variable: Systematic Risk

b. Linear Regression through the Origin

The results of Table 4-12 confirmed that there were two financial ratios including Account Profit Beta and Cash Flow Beta, which positively associated with Systematic Risk. As can be seen in Table 4-12, two predictors namely Account Profit Beta (B=1.334, Sig=0.002<0.05) and Cash Flow Beta (B=1.678, Sig=0.001<0.05) were all directly contributed in predicting Systematic Risk. As shown in Table 4-12, there is no significant relationship between Networking Capital and Assets with Systematic Risk. In addition, the results also indicated that Cash Flow Beta with highest coefficient value is the most important variable to predict Systematic Risk.

## Correlation between Systematic Risk and Account Profit Beta

Table 4-13 represents the correlation between Systematic Risk and Account Profit Beta. According to the following table, the correlation between Systematic Risk and Account Profit Beta is 0.352 with p-value of 0.003. Since, the p-value is lesser than 0.05 thus it can be stated that there is a positive significant relationship between Account Profit Beta and Systematic Risk.

Table 4: Correlation between Systematic Risk and Account Profit Beta

Systematic Risk

Account Profit Beta

Systematic Risk

Pearson Correlation

1

.352**

Sig. (2-tailed)

.003

N

70

70

Account Profit Beta

Pearson Correlation

.352**

1

Sig. (2-tailed)

.003

N

70

70

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

## Correlation between Systematic Risk and Cash Flow Beta

Table 4-14 represents the correlation between Systematic Risk and Cash Flow Beta. According to the following table, the correlation between Systematic Risk and Cash Flow Beta is 0.414 with p-value of 0.000. Since, the p-value is lesser than 0.05 thus it can be stated that there is a positive significant relationship between Cash Flow Beta and Systematic Risk.

Table 4: Correlation between Systematic Risk and Cash Flow Beta

Systematic Risk

Cash Flow Beta

Systematic Risk

Pearson Correlation

1

.414**

Sig. (2-tailed)

.000

N

70

70

Cash Flow Beta

Pearson Correlation

.414**

1

Sig. (2-tailed)

.000

N

70

70

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

## Correlation between Systematic Risk and Networking Capital

Table 4-15 represents the correlation between Systematic Risk and Networking Capital. According to the following table, the correlation between Systematic Risk and Networking Capital is 0.032 with p-value of 0.793. Since, the p-value is greater than 0.05 thus it can be stated that there is no significant relationship between Networking Capital and Systematic Risk.

Table 4: Correlations between Systematic Risk and Networking Capital

Systematic Risk

NWC

Systematic Risk

Pearson Correlation

1

.032

Sig. (2-tailed)

.793

N

70

70

NWC

Pearson Correlation

.032

1

Sig. (2-tailed)

.793

N

70

70

## Correlation between Systematic Risk and Assets

Table 4-16 represents the correlation between Systematic Risk and Assets. According to the following table, the correlation between Systematic Risk and Assets is 0.144 with p-value of 0.235. Since, the p-value is greater than 0.05 thus it can be stated that there is no significant relationship between Assets and Systematic Risk.

Table 4: Correlation between Systematic Risk and Assets

Systematic Risk

Assets

Systematic Risk

Pearson Correlation

1

.144

Sig. (2-tailed)

.235

N

70

70

Assets

Pearson Correlation

.144

1

Sig. (2-tailed)

.235

N

70

70

## Conclusion

In this chapter, the data were analyzed using descriptive statistics and multiple regressions. In order to carry out the multiple regressions the independent variables namely Account Profit Beta, Cash Flow Beta, Networking Capital, and Assets were regressed against Systematic Risk. The basic assumptions regarding multiple regression analysis were performed. According to analysis in this chapter, all the basic assumptions were met. As shown in this chapter, Accounting Profit Beta and Cash Flow Beta had significant positive relationship with Systematic Risk.