Agree or Disagree?

Discussion: discuss what is required to make causal statements in the context of regression analysis... In other words,what is required to be able to say that a particular independent variable, or treatment,causes the dependent variable?In your answer, discuss the role played by obtaining a random sample and random assignment of the "treatment" (in many cases, the treatment is the main independent variable).Once we obtain a satisfactory regression model, discuss potential sources of bias - e.g., not using the correct functional form, measurement error, omitted variable bias, the simultaneity problem, etc.Finally, what are some key considerations in selecting "control" variables in a multiple regression analysis.

Answer: What is required to make causal statements in the context of regression analysis?

A random sample - One important way is to ensure this is via a random sample. In our textbook, it provides explanation of how to choose random samples with population data and getting a true representative sample.

Also, our text highlights the problem of omitting variables either by accident or on purpose as omitting variables introduces the risk that your causality will be way off. The same can happen with a measurement error. Both control variables, any variable included in a regression equation whose purpose is to alleviate an endogeneity problem, and a proxy variable, a variable used in a regression equation in order to proxy for a cofounding factor, can improve causal interference.

When we don't have great controls or proxies to develop causality of one variable on another, we turn to instrumental variables, a variable that allows us to isolate the causal effect of a treatment on an outcome due to its correlation with the treatment and lack of correlation with the outcome.

Potential sources of bias:

I mentioned a few in my last answer but they mainly involve selecting the right sample, that is, it has to be random and representative of what you are trying to measure. Any sample that is nonrandom is known as a selected sample. Also, choosing the right functional form is important because we may end up skewing the causality. With determining function, we need to consider flexibility, precision, and exposition so using a quadratic function is useful. That is when you are reviewing more data to ensure you are establishing causality. The other previously mentioned bias that can occur are measurement error and omitted error. There is also simultaneity errors in which one or more of the treatments is determined at the same time as the outcome. This is where the level of treatment depends on the realization of the outcome.

Prince, J. (2019).Predictive analytics for business strategy: Reasoning from Data to Actionable Knowledge(1st ed.). Dubuque, New York: McGraw-Hill Education.