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Few questions on regression analysis

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1) Explain how we test independent against dependent variables in a regression analysis? What's the set up?
2) Does a correlation as presented in a regression analysis graph imply an actual casual relationship?
For example - can I say with a high degree of confidence "that on every full moon a chimpanzee will scratch itself" and say it was because there was a full moon?
3) How are regression analyses often misused / misinterpreted at work or in the news? Cite an example.

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This posting answers following question on regression analysis.

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Business, Other
Year 2
Statistics Questions
I need help understanding regression analysis:

Explain how we test independent against dependent variables in a regression analysis? What's the set up?

Regression analysis helps in understanding the impact of independent variable on dependent variable i.e. how much of variation in dependent variable is explained by the independent variables. This is generally done through Least Squares Method (OLS), where the squared error between actual and predicted values of the dependent variable is minimized.

The equation for regression analysis is set up in the following format:

Y = a + bX + e

Y = dependent variable, X = Independent variable
a = Intercept, b = ...

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