Main Concepts: Two-Variable Relationships

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 Main Concepts

• In this unit we are introducing the concept of a statistical model. A model is a set of assumptions about a variable or a relationship between variables. It is an idealization of reality which we hope approximates reality closely enough for our purposes. Or, as George Box, a well-known statistician, once said: "All models are wrong; some are useful."

• Models can be used for different purposes, including summarizing relationships, making predictions, and understanding phenomena.

• A surprisingly large number of interesting relationships can be modeled by a linear relationship.

• Regression is a very complex and subtle tool about which entire books have been written. We will very lightly scratch the surface in this course. We will return to this topic at the end of this course and scratch this surface once more.

• Correlation does not imply causation. Correlation merely measures the strength and direction of a linear relationship between two variables, which is a way of saying it tells us something about the predictive ability of a linear relationship.

• High correlation does not mean that the linear model is good and low correlation doesn’t mean that the linear model is inappropriate. The correlation coefficient measures the data's proximity to a straight line, but it does not measure the appropriateness of the linear model.

• In addition to learning to interpret models, we also study how well suited they are to answering our questions and how well model fits the data. Residual plots are useful tools for evaluating the fit of the model.