1. Math 174, Spring 2004 Trend Lines

2. The real world often does not provide us with formulas showing the relationship between two variables. Sometimes we need to come up with a mathematical model

3. Example (from text) A county Child Protective Services, CPS, agency has records showing the number of cases that it has handled during the years 1990- 1998. Use the table to predict the case load in 1999.

4. Data Example Year199019911992199319941995199619971998 Case Load 2373282528063534380843125067 53686445

5. Create a graph Plot each of the data points given and use a scatter plot IMPORTANT! Do not connect the points – we do not have a function! To make a trend line: 1. Right click on any point on the plot 2. Add a trend line 3. Choose which trend line you want 4. Go to options and display equation Let’s go to Case Load.xls that has our example graphed alreadyCase Load.xls

6. Trend Line for our example The function generated for our example is The independent variable for our function is t, which is the number of years since 1990 So, the expected case load in a year is f(y – 1990) Also notice that the trend line extends beyond the range of known dats This is called extrapolation – should be done with caution

7. Trend Lines What is a trend line? It is a function used to predict output values of a function (y-values) given an input value (x-value). How do you choose a trend line? 1. Look at the overall pattern 2. Try several types to see which fits best 3. Predict values of y using values of x close to the range of values in the plot The difference in choice of methods can be noticed over long periods of extrapolation