11.5 Choose the Best Model for Two-Variable Data

Goal  Choose the best model to represent a set of data.

Your Notes

Example 1
Use a linear model

Teacher’s Salaries The table shows the teacher’s salary y (in dollars) for a certain school district, where x is the number of years of teaching experience. Use a graphing calculator to find a model for the data.

x	1	2	3	4	
y	30,624	32,436	34,167	35,989	

x	5	6	7	
y	37,684	39,311	41,098	

1.	Make a scatter plot. The points lie approximately on a _line_. This suggests a _linear_ model.

2.	Use the _linear_ regression feature to find an equation of the model.

3.	Graph the model along with the data to verify that the model fits the data well.
A model for the data is y  _1739x  28,950_.

 Checkpoint Complete the following exercise.

1.	Use a graphing calculator to find a model for the data. Graph the model and data

x	0	1	2	3	
y	2	9	19	29	

x	4	5	6	7	
y	40	51	61	73	

y = 10.3x0.5

Your Notes

Example 2
Use an exponential model

Deer Population An environmental group observes a deer population in a park where hunting has been banned. The table shows the population y counted x years after the ban began. Use a graphing calculator to find a model for the data.

x	0	5	10	15	20	
y	500	729	1271	2206	3765	

Solution
1.	Make a scatter plot. The points are level at first and then begin to _rise_ rapidly. This suggests an _exponential_ growth model.
2.	Use the _exponential_ regression feature to find an equation of the model.
3.	Graph the model along with the data to verify that the model fits the data well.

A model for the data is y  _468(1.11)x.

Checkpoint Complete the following exercise.

2.	Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane.

x	1	2	3	4	5	6	7	
y	462	318	181	107	75	62	55	

y  598(0.686)x

Your Notes

Example 3
Use a quadratic model

Roller Coaster Riders A manager at a local amusement park kept a record of the number of people to ride the most popular roller coaster at the park. The table shows the number of people y that rode the roller coaster x hours after the park had opened. Use a graphing calculator to find a model for the data.

X	0	2	4	6	8	10	12	
Y	85	163	282	341	398	381	304	

Solution
1.	Make a scatter plot. The points form an _inverted U-shape_. This suggests a _quadratic_ model.
2.	Use the _quadratic_ regression feature to find an equation of the model.
3.	Graph the model along with the data to verify that the model fits the data well.

A model for the data is y _4.34x2  73.7x  62.8_.

 Checkpoint Complete the following exercise.

3.	Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane.

x	0	2	4	6	8	10	12	
y	100	178	273	314	349	324	289	

y  3.5x2  58.7x  90.8

Homework
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