7.7 choosing the best model for two-variable data p. 279
TRANSCRIPT
7.7 Choosing the 7.7 Choosing the Best Model for Best Model for
Two-Variable DataTwo-Variable Datap. 279p. 279
The following functions have been The following functions have been used to model a set of data. used to model a set of data.
To determine the best model for a To determine the best model for a set of data pts ( x , y ), make a set of data pts ( x , y ), make a scatter plot of the data and choose scatter plot of the data and choose the type of function suggested by the the type of function suggested by the pattern of the data pts. pattern of the data pts.
FunctionFunction General FormGeneral Form GraphGraph
Linear y a bx
FunctionFunction General FormGeneral Form GraphGraph
Quadratic 2a x cxy b
FunctionFunction General FormGeneral Form GraphGraph
Cubic 3 2y a bx xx c d
FunctionFunction General FormGeneral Form GraphGraph
Exponential
xy ab
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 3 Graph the model along with the data to verify that the model fits the data well.
ANSWER A model for the data is y = – 0.00793x2 + 0.727x + 13.8.
p. 280 #’s 1-3p. 280 #’s 1-3Plot the points to decide whichPlot the points to decide whichmodel works for the datamodel works for the data
Linear, Quadratic, or ExponentialLinear, Quadratic, or Exponential
p. 281 #’s 1 – 6p. 281 #’s 1 – 6