1/7/18 2.8: FITTING LINES TO CURVED RELATIONSHIPS WARM UP: Graph the following equation: Write the standard form of a quadratic equation: What kind of graph does it produce? If the relationship between two valuables is linear, we use a ______________________________________ line to model the relationship. For a NONLINEAR relationship, we can use a ____________________________ model to show the relationship. The quadratic model is: The graph of a quadratic model is: PROBLEM: Relationship between passing yards and age for 32 NFL quarterbacks in the 2010 season. Describe the relationship you see between the variables. How to calculate the quadratic model with a calculator: STEP 1: Enter data into Lists STEP 2: Create a scatterplot STEP 3: Choose Quadratic Regression 1) STAT CALC 5: QuadReg 2) ENTER 3) 2nd 1 , 2nd 2 , VARS Y-VARS 1: Function 1: Y1 4) ENTER 5) ENTER 6) Find a, b, c STEP 4: Zoom 9 Draw the line of regression and write the equation. We can also use an _____________________________ model. The standard form is: If b > 1, the graph shows: If 0 < b < 1, the graph shows: Sketch it here: Sketch it here: How to calculate the exponential model with a calculator: STEP 1: Enter data into Lists STEP 2: Create a scatterplot STEP 3: Choose Exponential Regression PROBLEM: A random sample of 14 golfers was selected from the 147 players on the LPGA tour. The total amount of money won during the year (in $) and the average number of strokes above 70 for each player in the sample were recorded (lower scores are better in golf). a) Calculate an exponential model for the data using adjusted scoring average as the explanatory variable b) Sketch the scatterplot, along with the exponential model. c) Calculate and interpret the residual for Lorena Ochoa, the last golfer on the list. CHOOSING BETWEEN QUADRATIC AND EXPONENTIAL MODELS In some cases, it is hard to tell if a quadratic model or an exponential model would be better to use. To decide, look at the ______________________________for both models and choose the model with the residual plot that has the most/least random scatter. (IOW the one that looks LEAST like an exponential or quadratic model) Super Bowl number versus cost of a 30s commercial Based on the residual plots below, which model is more appropriate? PROBLEM: Life insurance premiums depend on the type and amount of the policy as well as on personal characteristics like age, gender, and health status. The table shows monthly premiums (in dollars) for a 10-year term-life insurance policy worth $1,000,000 for people of various ages (in years). 1) Calculate a quadratic model for these data. 2) Calculate an exponential model for these data. 3) Given the plots of the residuals (below) which model is more appropriate? 4) Using your chosen model, calculate and interpret the residual for the 65-year-old.