1. Section 2:
Linear Regression

2. x y
Find the “best” linear equation representing the points of the scatter diagram.
Least-squares criterion – the sum of the squares of the vertical distances from the points to the line be made as small as possible.

3. Least Squares Line (Line of Best Fit, Regression Line)
y = a + bx b = a = = mean of y values = mean of x values

4. Example: For the data in the table, plot the scatter diagram
Example: For the data in the table, plot the scatter diagram. Find the regression line (line of best fit), and sketch the graph of the line.
x y
1 2
2 4
3 4
4 6

5. Standard Error of Estimate
measures the spread of a set of points about the least-squares line
denoted Se
Se =

6. Years of Experience (x)
Example
Years of Experience (x)
Salary (y) 12 29 16 31 6 23 34 27 38 8 24 5 22 19 36 13 33

7. Example (Continued) y = 19.47 + .71x y = 19.47 + .71(15) = 30.12
Compute a Confidence Interval 95% (for x =15)
y = (15) = 30.12