Section 2: Linear Regression.

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Presentation transcript:

Section 2: Linear Regression

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.

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

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

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

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

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