1. Introduction to regression 3C. Least-squares regression

2. Another method for finding the equation of a straight line is the least-squares regression. Least-squares works by mathematically balancing the distance that points are away from the regression line. Easy to work out using CAS calculator.

3. Using CAS Input data into spreadsheet on Lists & Spreadsheet. Create scatterplot in Data & Statistics Then, – MENU – 4: Analyse – 6: Regression – 1: Show Linear (mx+b) – [or 2: Show Linear (a+bx)]

4. To find r and r 2 – Go back to Lists & Spreadsheet page – MENU – 4: Statistics – 1: Stat Calculations – 3: Linear Regression (mx+b) – Fill in the table with X List as the independent variable and Y List as the dependent variable.

5. Example Exercise 3C, Q.1 Then, you do Q.2 and Q.3

6. Calculating least-squares regression by hand If you are given a summary of the data rather than the data itself, you may need to calculate the least-squares regression by hand.

7. Summary data: – the mean of the independent variable – the mean of the dependent variable – s x the standard deviation of the independent variable – s y the standard deviation of the dependent variable – r Pearson’s product-moment correlation coefficient

8. The formulae The general form of the least-squares regression line is where: – The slope of the regression line is – The y-intercept of the regression line is

9. Example Ex 3C, Q.4 Then, you do – 5(a)(d), 7, 10, 11, 12, 13