Linear Regression. Determine if there is a linear correlation between horsepower and fuel consumption for these five vehicles by creating a scatter plot.

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Presentation transcript:

Linear Regression

Determine if there is a linear correlation between horsepower and fuel consumption for these five vehicles by creating a scatter plot and calculating the correlation coefficient.ExampleExample Vehicle HorsepowerFuel Consumption Midsize sedan Minivan Small sports utility vehicle Midsize motorcycle Luxury Sports car

Regression  analytic technique for determining a relationship between a dependent variable and an independent variable. If two variables have a linear correlation, you can use a simple mathematical model of the relationship by looking at the line of best fit. Find the equation of the line to make predictions by INTERPOLATION (estimating between data points) and EXTRAPOLATION (estimating beyond the range of the data).

When a correlation is strong, it is easy to draw a line of best fit. But if it is more complex, an analytic method called the least-squares fit must be used. The equation to use is: where and This formula looks complex, however it is not that bad if you organize your answer. You may sometimes see a and b reversed depending on the book that you read. Once you get the equation, you can place it on your graph.

Age (years)Annual Income($000) xy Find the equation for the line of best fit. Place two more columns on the table (x 2 )(xy) and sum up each column.

How do outliers effect the line of best fit? Homework Pg 180 # 1,2,5,7

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