5.7 Predicting with Linear Models

Objective : Deciding when to use a linear modelObjective : Use a linear model to make a real life prediction.

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A good way to decide whether data can be representedby a linear model is to draw a scatter plot of the data.

You are a restaurant owner and are making a menu with new pricing. You wantthe menu to last 3 years. By how much would you increase the prices so that theywill keep up with increases in costs over the next 3 years?

The manager of the restaurant made the following table and scatter plot.

Year Fish Meat

1991

3 .75 2.50

1993

6.15

2.70

1995

5.25 3.00

1997

4.05 3.30

1999

8.75 3.50

Average price per pound.

Average price per pound in

$

0

1

2

3

4

5

6

7

8

9

Year

1991 1993 1995 1997 1999

Fish in blueMeat in red

Draw a line of best fit for meat. There is not a good line for fish

When you use a linear model to estimate data points thatare not given, you are using linear interpolation or linearextrapolation.

Linear interpolation is a method of estimating the coordinates of a point that lies between two given data points.

Example: Go back to the graph and estimate the price per pound of meat in 1998.

Linear extrapolation is a method of estimating thecoordinates of a point that lies to the right or left of the given data.

Example: Go back to the graph and estimate the price per pound of meat in 2003.

About $3.40 per lb

About $4.00 per lb