1. 5.7 Predicting with Linear Models Objective : Deciding when to use a linear model Objective : Use a linear model to make a real life prediction. 1 2 A good way to decide whether data can be represented by a linear model is to draw a scatter plot of the data.

2. You are a restaurant owner and are making a menu with new pricing. You want the menu to last 3 years. By how much would you increase the prices so that they will 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 19911993199519971999 Fish in blue Meat in red Draw a line of best fit for meat. There is not a good line for fish

3. When you use a linear model to estimate data points that are not given, you are using linear interpolation or linear extrapolation. 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 the coordinates 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