# 7.7 Choosing the Best Model for Two-Variable Data p. 279.

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7.7 Choosing the Best Model for Two-Variable Data p. 279

 The following functions have been used to model a set of data.  To determine the best model for a set of data pts ( x, y ), make a scatter plot of the data and choose the type of function suggested by the pattern of the data pts.

Function General Form Graph Linear

Function General Form Graph Cubic

Function General Form Graph Exponential

EXAMPLE 1 Use a linear model Tuition The table shows the average tuition y (in dollars) for a private four-year college in the United States from 1995 to 2002, where x is the number of years since 1995. Use a graphing calculator to find a model for the data.

EXAMPLE 1 Use a linear model SOLUTION STEP 1 Make: a scatter plot. The points lie approximately on a line. This suggests a linear model. STEP 2 Use: the linear regression feature to find an equation of the model.

EXAMPLE 1 Use a linear model STEP 3 Graph: the model along with the data to verify that the model fits the data well. A model for the data is y = 933x + 14,600. ANSWER

EXAMPLE 2 Use an exponential model Cooling Rates You are storing leftover chili in a freezer. The table shows the chili’s temperature y (in degrees Fahrenheit) after x minutes in the freezer. Use a graphing calculator to find a model for the data.

EXAMPLE 2 Use an exponential model SOLUTION STEP 1 Make: a scatter plot. The points fall rapidly at first and then begin to level off. This suggests an exponential decay model. STEP 2 Use: the exponential regression feature to find an equation of the model.

EXAMPLE 2 Use an exponential model SOLUTION STEP 3 Graph: the model along with the data to verify that the model fits the data well. A model for the data is y = 98.2(0.969) x.ANSWER

EXAMPLE 3 Use a quadratic model Fuel Efficiency A study compared the speed x (in miles per hour) and the average fuel efficiency y (in miles per gallon) of cars. The results are shown in the table. Use a graphing calculator to find a model for the data.

EXAMPLE 3 Use a quadratic model SOLUTION STEP 1 Make a scatter plot. The points form an inverted U-shape. This suggests a quadratic model. STEP 2 Use the quadratic regression feature to find an equation of the model.

EXAMPLE 3 Use a quadratic model STEP 3Graph the model along with the data to verify that the model fits the data well. ANSWER A model for the data is y = – 0.00793x 2 + 0.727x + 13.8.

p. 280 #’s 1-3 Plot the points to decide which model works for the data Linear, Quadratic, or Exponential p. 281 #’s 1 – 6

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