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If an independent variable is correlated with the error term, we can use the independent variable to predict the error term, which violates the notion that the error term represents unpredictable random error. We need to find a way to incorporate that information into the regression model itself.
Is Beta same as correlation?
Beta tries to measures the effect of one variable impacting the other variable. Correlations measure the possible frequency of similarly directional movements without considerations of cause and effect. Beta is the slope of the two variables. Correlation is the strength of that linear relationship.
Is the independent variable called an explanatory variable?
If the independent variable is referred to as an “explanatory variable” then the term “response variable” is preferred by some authors for the dependent variable. From the Economics community, the independent variables are also called exogenous .
Why are the explanatory variables not observed without error?
With the way the explanatory variables enter into the formulas for the estimates of the \\(\\beta \\,\\)’s, the random errors in the explanatory variables do not cancel out on average. This results in parameter estimators that are biased and will not approach the true parameter values no matter how much data are collected.
What is the difference between a response variable and an explanatory variable?
A response variable is the particular quantity that we ask a question about in our study. An explanatory variable is any factor that can influence the response variable.
How is the explanatory variable used in an experimental study?
In those cases, the explanatory variable is used to predict or explain differences in the response variable. In an experimental study, the explanatory variable is the variable that is manipulated by the researcher.