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Scatter plots and Regression Algebra II

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Linear Regression Linear regression is the relationship between two variables when the equation is linear. This is the equation for “best fit” (y = ax +b)

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Non-linear Regression These will mostly be quadratic and exponential. But, may also be logarithmic or other powers, like cubic or square root.

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Which model would best fit each graph?

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Entering Data in Calculator From menu, go to STAT Enter x-values in L1 and y-values in L2. (To delete lists, arrow up to top of list, hit F6, then F4 (Del-A). To graph, hit F1 (GRPH), then F1 (GPH1). If GRPH is not on your options, hit F6 first. Determine the model for your regression. Then, hit F1 (Calc) and choose your model. From the equation screen, hit F6 (Draw) to draw the regression line on your graph.

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Types of Models in Calc X = linear (y = ax + b) X^2 = quadratic (y = aX 2 + bx + c) X^3 = cubic (y = aX 3 + bx 2 + cx + d) Log = logarithmic (y = a + b*ln(x)) Exp = exponential (y = a*e (bx) ) Pwr = power (y = a*x b )

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Example 1 A study compared the speed x (in miles per hour) and the average fuel economy y (in miles per gallon) for cars. The results are shown in the table. What type of model is represented by the scatter plot? Find an equation to best fit the data. Predict the mpg if the speed is 90 mph.

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Example 2 The data below shows the number of facebook users each year. Based on the scatter plot, what model best fits the data? Write an equation to represent the data. Predict how many users there were in 2012. Year2004200520062007200820092010 Users (millions) 15.51250100350550

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