The predicted value can be found by the least squares regression equation of a line, which is \widehat{y} = a+bx where x is the independent/ explanatory variable which lies on the x-axis, y is the dependent/response or the observed variable which lies on the y-axis, and \widehat{y} is the predicted value. Recall that** a **is the y-intercept and

**is the slope of the line.**

*b*a. The predicted value when *x = 60* is \widehat{y} = 32 + 0.4 \times 60 = 56.

b. The residual is the difference between the observed value and the predicted value.

Residual y - \widehat{y} = 52 - 60 = -4.

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How to find the **least**-**squares regression line** - **AP Statistics**

**Regression** tests seek to determine one variable's ability to predict another
variable. In this **analysis**, one variable is dependent (the one predicted), and the
other is ...

For more information, see How to find the **least**-**squares regression line** - **AP Statistics**