I'm not certain—so don't take me at 100% here—but it doesn't feel right to me. Predicting y/x by x itself is strange. Of course you are going to get a significant prediction, because x is used to calculate the DV. I generated some random data (assuming no relationship between any of the variables)...
set.seed(1839) # setting seed for replicability
ebit <- sample(1:7, 200, T) # creating ebit scores
assets <- sample(1:7, 200, T) # creating assets scores
age <- sample(1:7, 200, T) # creating age scores
data <- data.frame(roa=ebit/assets, ebit, assets, age) # making dataset
and ran the models:
summary(lm(roa~assets+age, data)) # running roa as DV
Call:
lm(formula = roa ~ assets + age, data = data)
Residuals:
Min 1Q Median 3Q Max
-1.8400 -0.6483 -0.0154 0.4882 4.3598
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.32694 0.22118 15.042 <2e-16 ***
assets -0.44517 0.03770 -11.807 <2e-16 ***
age -0.04832 0.03768 -1.282 0.201
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.025 on 197 degrees of freedom
Multiple R-squared: 0.4189, Adjusted R-squared: 0.413
F-statistic: 71 on 2 and 197 DF, p-value: < 2.2e-16
And
summary(lm(ebit~assets+age, data)) # running ebit as DV
Call:
lm(formula = ebit ~ assets + age, data = data)
Residuals:
Min 1Q Median 3Q Max
-3.0695 -1.7712 0.1377 1.4421 3.5400
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.35110 0.43397 7.722 5.66e-13 ***
assets 0.04386 0.07398 0.593 0.554
age 0.06503 0.07393 0.880 0.380
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.011 on 197 degrees of freedom
Multiple R-squared: 0.005828, Adjusted R-squared: -0.004265
F-statistic: 0.5774 on 2 and 197 DF, p-value: 0.5623
The effect of assets
on roa
makes sense in the first model. All it says is: As the denominator gets higher, the value of the quotient gets lower. How does that help you? The second model is more straightforward: It is the effect of assets
and age
on ebit
simultaneously.