Ekstrom Math 115b Mathematics for Business Decisions, part II Trend Lines Math 115b.
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Mathematic Trend Lines Math 115b
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Transcript of Ekstrom Math 115b Mathematics for Business Decisions, part II Trend Lines Math 115b.
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 1998-2006. Use the table to predict the case load in 2010.
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.
Year 1998 1999 2000 2001 2002 2003 2004 2005 2006Case Load 2,373 2,825 2,806 3,534 3,808 4,312 5,067 5,368 6,445
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
tetf 1217.06453.2373)(
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 2010.
There will be a predicted 10,225 cases in the year 2010.
By how much would a linear model differ?
Example (from Text)
225,10
6453.2373
)19982010()12(
6453.2373)(
121217.0
1217.0
e
ff
etf t
