Ekstrom Math 115b Mathematics for Business Decisions, part II Trend Lines Math 115b

Ekstrom Math 115b Trend Lines  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 Trend Lines

Ekstrom Math 115b Trend Lines  A county Child Protective Services, CPS, agency has records showing the number of cases that it has handled during the years Use the table to predict the case load in  Graph can be found in Case Loads.xls Example (from Text)

Ekstrom Math 115b Trend Lines Data Example * Enter this as two COLUMNS, not rows. In Column A, enter in the years, as years since 1998, and in Column B, enter in the case loads.

Ekstrom Math 115b Trend Lines  Plot each of the data points given and use a scatter plot  IMPORTANT! Do not connect the points – we do not yet have a known continuous function!  To make a trend line:  Right click on any point on the plot  Add a trend line  Choose which trend line you want  Check “Display equation on chart”  Can also format trend line to extrapolate information Create a Graph

Ekstrom Math 115b 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?  Look at the overall pattern  Try several types to see which fits best  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 Trend Lines

Ekstrom Math 115b Trend Lines  The function generated for our example is  The independent variable for our function is t, which is the number of years since 1998  So, the expected case load in a year is f (y – 1998)  Also notice that the trend line extends beyond the range of known dates  This is called extrapolation – should be done with caution Trend Line for our Example

Ekstrom Math 115b Trend Lines  Two things to look for:  Data Fit:  How well does the trend line fit the data?  Looking for the minimum distance between the line and ALL* of the data points.  Predictive Power  Does the trend line look reasonable past the last data point?  Long term? Short term? What Makes a Good Trend Line?

Ekstrom Math 115b Trend Lines  Using the table of CPS cases, predict the case load in  There will be a predicted 10,225 cases in the year  By how much would a linear model differ? Example (from Text)