Ch 9.2: Linear Regression

*y* represents the

*observed* y-value for a data point

Is it appropriate to use a regression line to predict​ y-values for​ x-values that are not in​ (or close​ to) the range of​ x-values found in the​ data?

It is not appropriate because the regression line models the trend of the given​ data, and it is not known if the trend continues beyond the range of those data.

Given a set of data and a corresponding regression​ line, describe all values of x that provide meaningful predictions for y

Prediction values are meaningful only for​ x-values in​ (or close​ to) the range of the original data.

In order to predict​ y-values using the equation of a regression​ line, what must be true about the correlation coefficient of the​ variables?

The correlation between variables must be significant.

*x(bar)* represents the

average of *all x-values*

*y(bar)* represents the

average of *all y-values*

*y(hat)* represents the

predicted y-value (on a regression line)

residual (*di*)

the difference between the *observed* y-value and the *predicted* y-value (can be positive, negative, or 0)

regression line (*line of best fit*)

the line for which the sum of the squares of the residuals is a minimum

the regression line *always passes through point* ...

x(bar), y(bar)

equation of a regression line

y(hat) = mx + b