A theory specifies that the leverage ratio of a firm increases with its firm siz

Question

A theory specifies that the leverage ratio of a firm increases with its firm size, decreases with market-to-book equity ratio, and increases with profitability. Using Ordinary Least Squares estimation based on 20 firm observations to test this theory, a regression equation is written as: L, = 0.4 1 1 + 0.0235,-0.547(M / B), + 0. | 02 EPS, + residual, , (0.055) (0.009) (0.201) (0.075) R2 = 0.02 where Li is the book value of debt divided by total assets of firm i, S, is the log of total sales of firm i for measuring firm size, M/B, is the market value of equity divided by book value of equity of firm i, and EPS, is the earnings per share of firm i for measuring profitability. The figures in parentheses below the coefficient estimates are estimated standard errors.

Explanation / Answer

Here Li is dependent variable and Si, M/B and EPSi are independent variables.

Given that the regression equation is,

Li = 0.411 + 0.023Si - 0.547*M/B + 0.102EPSi

intercept = 0.411

slopes = 0.023, -0.547 and 0.102

Interpretation of slope :

If we fix M/B and EPSi then one unit change in Si will be 0.023 unit increase in Li.

If we fix EPSi and Si then one unit change in M/B will be 0.547 unit decrease in Li.

If we fixed Si and M/B then one unit change in EPSi will be 0.102 unit increase in Li.

ALso we have given standard errors of the slope.

SE(intercept) = 0.055

SE(Si) = 0.009

SE(M/B) = 0.201

SE(EPSi) = 0.0705

Now we can test here individual significance.

The test of hypothesis is,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for independent variable.

Assume alpha = level of significance = 0.05

Here test statistic follows t-distribution with n-2 degrees of freedoms.

The test statistic is,

t = b / SE(b)

where b is sample slope

and SE(b) is standard error for estimate.

Also we need here p-value for taking the decision.

P-value we can find in EXCEL.

syntax :

=TDIST(x, deg_freedoms, tails)

where x is absolute value of test statistic

deg_freedom = n-2 = 20-2 = 18

tails = 2

Now we find test statistic and p-value for three variables.

Now we can see that Si and M/B are significant variables since P-value < alpha and EPSi is insignificant variable.

R-sq = 0.02

It expresses the proportion of variation in dependent variable which is explained by variation in independent variables.

b SE(b) t p-value Si 0.023 0.009 2.56 0.0199 M/B -0.547 0.201 -2.72 0.0140 EPSi 0.102 0.075 1.36 0.1906

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