From the coefficients of the original logistic regression, and ignoring the likelihood ratio tests, is it generally true that firms with a higher current ratio are more likely to go into liquidation? Explain.
In the evaluation of corporate liquidations, a logistic regression is used. Based on historical data, a firm is assigned a value one if it goes into liquidation the following year, and zero if it does not. Computer output shows:
Logistic regression results Coefficient Probability
Constant 1. 0 not given
Return on capital employed 0. 4 0.04
Gearing +0. 1 0.40
Turnover ratio + 0.3 0.70
Current ratio 0.2 0.01
Retained earnings/total assets 0. 6 0.52
The above probabilities are derived from likelihood ratio tests.
Firm X, which is not in the original sample, has values of:
Return on capital employed 0.1
Gearing + 0.6
Turnover ratio + 1.5
Current ratio 0.1
Retained earnings/total assets 0.4
(a) State whether gearing is a dependent variable or an independent variable
of the logistic regression. (1 mark)
(b) According to the logistic regression, determine the probability that Firm X
is likely to go into liquidation in the following year. (10 marks)
(c) From a table (not shown) representing a correlation matrix, you find that
return on capital employed and retained earnings/total assets have a correlation coefficient of 0.6, compared with other coefficients which are all less than 0.4 in absolute terms. Bearing in mind the correlation matrix and the likelihood ratio tests, which one variable might you consider removing and why? (8 marks)
(d) A table of residuals shows two entries:
Row 46 indicates a Pearson’s residual is 3.2.
Row 104 indicates a Pearson residual of 9.5.
Which of these two outliers creates more of a problem for the fitted model?
(e) From the coefficients of the original logistic regression, and ignoring the likelihood ratio tests, is it generally true that firms with a higher current ratio are more likely to go into liquidation? Explain. (6 marks)
(f) Taking into account the likelihood ratio tests, is your conclusion from
part (e) statistically significant at the 95% confidence level or not?
(g) Bearing in mind both the logistic regression coefficients and the likelihood ratio tests, state:
(1) whether a firm with a lower, but positive, return on capital employed is more likely to go into liquidation, (3 marks)
(2) whether a firm with a lower, but negative, return on capital employed is more likely to go into liquidation, and (3 marks)
(3) whether the above two results are statistically significant, at the 95% level of confidence.