Introduction to regression 3C. Least-squares regression.

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Presentation transcript:

Introduction to regression 3C. Least-squares regression

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.

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)]

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.

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

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.

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

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

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