# Trendline

advertisement ``` Studies of the metabolism of alcohol consistently show
that blood alcohol content (BAC), after rising rapidly
after ingesting alcohol, declines linearly.
 For example, in one study, BAC in a fasting person rose
to about 0.018 % after a single drink. After an hour
the level had dropped to 0.010 %. Assuming that BAC
continues to decline linearly (meaning at a constant
rate of change), approximately when will BAC drop to
0.002%?
 Need to make an equation and then use the equation
to answer the question (make a prediction)
 Define the variables and assign each a letter to
represent it
 We can make it a table for fun
 Make the equation (y intercept)
 y = -.008x + .018
 Make predictions!
 The question is &quot;when will the BAC reach .002%?“
 Plug in .002 for Y and solve for X.
 .002 = -.008x + .018
 -.016 = -.008x
 x = 2 hours
 Therefore the BAC will reach .002% after 2 hours.
 What if the data isn’t perfectly linear?
 Can use trendlines – make predictions
 Interpolations / extrapolations
 Women’s world records
 Trendline - estimate of a linear function that fits the
data
 Legend – identifies what the dots on the chart
represent. For two variable graphs we don’t really need
this
 Title + axes – always have these labeled
 Source
What is the projected record in 1999?
By equation
Trendline estimate
Data points – 7 data points is good, lower than this is
not as good.
2. R squared (r2)
1.
1.
2.
3.
4.
This is a measure of strength of the linear relationship
between x and y.
.7 to 1 typically indicates a strong linear relationship
.4 - .7 is more moderate linear relationship
&lt; .4 is weak and probably shouldn’t be used to make a
prediction
3.
Practical / Physical / Social / Political Sense ??
- Think about your prediction. What outside factors
could affect it?
- How far away from the data is your prediction?
 What will be the record in 2100?
 What was the record in 500?
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