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 "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 < .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?