# Univariate regression analysis - unexpected sign

I am performing an univariate regression analysis by basically regressing a default rate on macro economic variables such as

$DR = \alpha + \beta GDP$

I noticed that sometimes the sign of the betas does not correspond to the economic intuition but when I add some other macro variables (unemplyoment, interest rate), then this variable has a economically intuitive sign.

I was wondering if considering such variable can be problematic ? What is the literature saying about this.

Moreover, concerning the p-value, could be also consider variables that are not significant in the univariate analysis?

• Relevant answer. Jul 31, 2018 at 23:58

Once you add one more regressors, your coefficient $\beta$ will always change if the new variable is correlated with the dependent variable and the other independent variable.
$$DR = \alpha + \tilde{\beta} GDP + \gamma Unemp + e$$
then your initial $\beta$ will be:
$$\newcommand{\Var}{\operatorname{Var}} \newcommand{\Cov}{\operatorname{Cov}} \beta = \tilde{\beta} + \gamma \frac{\Cov(GDP,Unemp)}{Var(Unemp)}.$$