Liquidity and Profitability Analysis by using simple rank correlation:In the following table the relationship between liquidity and profitability is analyzed with the help of rank correlation.Source: Financial statements of TEPL (calculated values)Table4:YearCATACEEBITCATA%Rank on CATA(x1)Return on CE%Rank on ROCE(x2)d=x1-x2d^2=(x1-x2)^2

200612240646130644441306444410076993.6930.58-525

20078001458868646919554029962992.1162.67-11

20081162998612561571250672545453692.58512.5324

20091210143113207411332578767015791.63813.72636

201038605820395374055686767143474997.64117.2100

2011469031375017813750178137430751793.4745.95-11

2012376818804143651741436517530704590.9498.84525

2013465576284924779149247791187502394.5422.66-416

2014291153333190568531905685179451291.2570.49-24

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The relationship between liquidity (measured by CATA) and profitability (measured ROCE) of TEPL over the period of 9 years is presented in Table-4. This relationship is established by using Spearman's Rank Correlation Coefficient. The rank correlation between Current assets to Total assets (CATA) and Return on Capital Employed (ROCE) is computed by applying the formula r (rank) =1-(6 sigma (d2)/n(n2-1) where d=difference in rank and n = number of pairs of observations. Putting the respective values of d and n in rank correlation formula above we obtain r = 0.067 which indicates that there is a low positive correlation between liquidity and profitability of the company. To find out the significance of the above result we test the hypothesis as under:Null Hypothesis: There is no significant direct relationship between Liquidity and Profitability of TEPL i.e. p=0.Alternate Hypothesis: There is a significant direct relationship between Liquidity and Profitability of TEPL i.e. p0tp,n-2 =r*under root (n-2)/under root (1-r2)By substituting the values of n=9 and r=0.067 we get t=0.18.Since computed value of t (0.18) is less than the table value of t (i.e. 2.365 at 5% level and 3.499 at 1% level of significance), the null hypothesis, H0: p=0 is accepted both at 5% and 1% level of significance and thus, the alternative hypothesis, H1:p 0 is rejected both at 95% and 99% level of confidence. Therefore, we may conclude that there is no direct significant relationship between liquidity and profitability of the firm under study. This relationship is not statistically significant both at 5% and 1% level. Multiple Regression Analysis:In order to find out the influence of liquidity ratios under consideration on profitability of the firm the following linear multiple regression model is used where Dependent variable is y and independent variables are (x1, x2, x3, x4, x5, x6)y = Return on Capital Employed (ROCE),x1= Current Ratio (CR),x2= Quick Ratio (QR),x3= Current assets to Total assets (CATA),x4= Working Capital Turnover Ratio (WCTR),x5= Inventory Turnover Ratio (ITR) and x6= Debtors Turnover Ratio (DTR). In this study CR, QR, CATA, WCTR, ITR and DTR have been taken as the explanatory variables and ROCE has been used as the dependent variable. For selecting the explanatory variables the correlation matrix is constructed giving the correlation coefficients between the explanatory variables and the dependent variables. It revealed that there is a strong correlation between all the variables and are used in multiple regression analysis.

Liquidity and Profitability Analysis by Using Linear Multiple Regression.YearReturn on CE(y)CR(x1)QR(x2)ROTA(X3)WCTR(x4)ITR(x5)DCR(x6)

20060.00501.80.680.00310.492.132.39

20070.02601.190.970.0067.353.061.75

20080.12501.130.830.02410.116.032.69

20090.13701.260.980.0365.824.852.353

20100.17201.121.030.02411.3916.755.93

20110.05901.111.040.05922.6232.215.13

20120.08801.631.060.0882.384.251.72

20130.02601.270.880.0265.073.676.24

20140.00401.390.760.0395.393.227.85

The multiple regression equation isY=b0+b1x+b2x2+b3x3+b4x4+b5x5+b6x6 where b1, b2..........., b6 are the coefficients of x1, x2,, x6.The output of the multiple regression is shown in the below picture.The Multiple Regression is performed by using SAS 9.2 version and by writing the codeThe code used was:Proc reg data= work. Analysis;Model ROCE=CR QR CATA WCTR ITR DCR;run;quit; Here Analysis is the Input Data set and Work is the Temporary Location of storing Data files and when the regression was performed the output was as follows

From the output the multiple regression equation is Y=3.43-0.26x1-2.32x2-4.23x3-0.13x4+0.09x5-0.09x6R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:R-squared = Explained variation / Total variationR-squared is always between 0 and 100%: 0% indicates that the model explains none of the variability of the response data around its mean. 100% indicates that the model explains all the variability of the response data around its mean.R2 in this model is 98.16% which indicates that 98.16% of variation in dependent variable Return on Capital Employed is explained by the six Independent variables (Current Ratio (CR), Quick Ratio (QR),Return on Total Assets (ROTA), Working capital Turnover Ratio (WCTR), Inventory Turnover Ratio (ITR), Debtors Conversion Ratio (DCR))You can calculate a regression equation by using the same number of data points as you have equation coefficients. However, the regression equation will not be as universal as a regression equation calculated using three times the number of data points as equation coefficients.To correct theR2for such situations, an adjustedR2takes into account the degrees of freedom of an equation. When you suspect that anR2is higher than it should be, calculate theR2and adjustedR2. If theR2and the adjustedR2are close, then theR2is probably accurate. IfR2is much higher than the adjustedR2, you probably do not have enough data points to calculate the regression accurately.The formula for adjustedR2:AdjustedR2==92%Wherenis the number of data points andmis the number of independent variables.Then in the output the t value for all the independent variables or Parameter estimates is greater than 1.96 at 95% Level of Significance. It indicates that all the independent variables are significantly contributing in explaining the dependent variable.The multiple correlation coefficient of ROCE on CR, QR, CATA, WBTR, ITR and DTR is 0.98 which reveals that the profitability of the firm was highly influenced by those explanatory variables. The value of R2 indicates that the explanatory variables taken together contributed about 98% of the variations in the profitability of the company. The regression analysis results also show that goodness of fit of the regression equation is statistically significant at 5% level.