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 = 40* is \widehat{y} = 18 + 0.25 \times 40 = 28. So Mary's predicted value is 28.

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

Residual y - \widehat{y} = 32 - 28 = 4. So Mary's residual is 4.

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Business **Statistics** - QBM117 **Least squares regression**. - ppt ...

**Regression**:**prediction** of one variable from another w Linear **regression analysis**
can ... 6 Finding a **line** which best summarises the data w We **find** the **line** which
has the ... 12 w **Predicted value** comes from **Least**-**Squares Line** For example,
**Mary** (with ... **AP STATISTICS** LESSON 3 – 3 **LEAST** – **SQUARES REGRESSION**.

For more information, see Business **Statistics** - QBM117 **Least squares regression**. - ppt ...