The Least-Squares Line Introduction

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Presentation transcript:

The Least-Squares Line Introduction

Many lines appear to fit the data well. Source: http://www.studyworksonline.com, 8/13/03

Many lines appear to fit the data well. Source: http://www.studyworksonline.com, 8/13/03

Many lines appear to fit the data well. Source: http://www.studyworksonline.com, 8/13/03

Many lines appear to fit the data well. Source: http://www.studyworksonline.com, 8/13/03

Many lines appear to fit the data well. Source: http://www.studyworksonline.com, 8/13/03

Many lines appear to fit the data well. There is one line that is often said to fit the best (especially when there are no outliers) The Least Squares Line Error2 Source: http://www.studyworksonline.com, 8/13/03 Actual Actual – Predicted = Error Predicted

Source: http://www.studyworksonline.com, 8/13/03

Least-Squares Line The Least Squares Line is the line that minimizes the sum of the squares of the errors. Source: http://www.studyworksonline.com, 8/13/03

Least-Squares Line We have qualitative ways of expressing how appropriate the linear model is like “a very appropriate model”, or “ a fairly appropriate model”, or “ an inappropriate model”. There is also a quantitative way to express the “goodness of fit” called the correlation coefficient, r. The correlation coefficient, r, measures the strength of the linear relationship between the two variables.

The Least-Squares Line Introduction

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