Question

Explain the difference between a univariate OLS model with a highly statistically significant coefficient on the X variable, and a univariate OLS model with a high R-squared. How do both concepts relate to inferring meaning from statistics?

Answer 1

>> In a univariate OLS model

>> a highly statistically significant coefficient on the X variable, mean that the coefficient is not equal to zero and that there exists a relationship between an independent and dependent variable. This tells us the causation effect

>> On the other hand, a high R-squared mean that a large amount of variability in dependent variable y is explained by independent variable x and there is no good need of including other variables into account.

>> Both a significant coefficient and high R square is good for chooosing a statistically robust model