With correlation, all we can measure is the relative strength of an association and whether it is statistically significant. With regression, we can model that association in a linear form and predict values of *Y* given the values of *X*.

After completing this chapter, you will be able to

- specify the equation format for a simple linear regression model,
- define residuals (errors),
- fit a linear regression line by eye,
- describe how fitting the regression line by minimizing residuals works,
- use the fitted regression model to make predictions of
*y*, based on the values of*x*, - interpret residual plots,
- determine the confidence interval for the slope of a regression line.

The simple form of a linear regression model is as follows:

*y* = *ax* + *b*

We read this as “*y* equals *a* times *x*, plus a constant *b*.” You will note that this is the equation for a line with slope *a* and intercept *b*. The value *a* is also termed the *coefficient for x* (Figure 11.1). The constant *b* is where the regression line intersects the y-axis and is also called the y-intercept.

Using the baseball payroll example and assuming that a correlation exists between the payroll amount in dollars and the number of wins over three seasons, can we predict wins based on a given payroll amount?

On the basis of Figure 11.2, it appears that an ...

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