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Scatter plots and Regression. Algebra II. 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). Non-linear Regression. These will mostly be quadratic and exponential.
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Scatter plots and Regression Algebra II
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)
Non-linear Regression • These will mostly be quadratic and exponential. • But, may also be logarithmic or other powers, like cubic or square root.
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.
Types of Models in Calc • X = linear (y = ax + b) • X^2= quadratic (y = aX2 + bx + c) • X^3 = cubic (y = aX3 + bx2 + cx + d) • Log = logarithmic (y = a + b*ln(x)) • Exp = exponential (y = a*e(bx)) • Pwr = power (y = a*xb)
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.
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.