1. Scatter plots and Regression Algebra II

2. 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)

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

4. Which model would best fit each graph?

5. 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.

6. 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 )

7. 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.

8. 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