Understanding Line of Fit in Data Analysis
Line of fit is used in data analysis to model data with an approximate linear relationship. Through examples, you can learn how to find a line of fit, create scatter plots, sketch fitting lines, and estimate values based on the line of fit equation.
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Do Now Plot these points x 1 2 4 4 5 6 7 10 y 16 14 11 10 5 2 3 2 18 16 14 12 10 8 6 4 2 0 0 2 4 6 8 10 12
Finding Line of Fit Algebra 2- Period 7
What is a line of fit? Why use it? Data do not always show an exact linear relationship. When the data in a scatter plot show an approximately linear relationship, you can model the data with a line of fit.
Finding a Line of Fit (Example 1) Femur length (x) 40 45 32 50 37 41 30 34 47 45 Height (y) The table shows the femur lengths (in centimeters) and heights (in centimeters) of several people. Do the data show a linear relationship? If so, write an equation of a line of fit and use it to estimate the height of a person whose femur is 35 centimeters long. 170 183 151 195 162 174 141 151 185 182
Example 1 Continued Step 1: Create a scatter plot 200 180 160 140 120 Height 100 80 60 40 20 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Femur Length Does the graph seem linear?
Example 1 Continuedstill Step 2: Sketch the line that most closely appears to fit the data. There are multiple possibilities. 200 180 160 140 120 Height 100 80 60 40 20 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Femur Length
Example 1 Continuedagain Step 3: Choose two points on the line. For the line shown, you might choose (40,170) and (50,195). Step 4: Write an equation of the line.
Example 1 ContinuedYes I Know Use the equation to estimate the height of the person. The approximate height of a person with a 35 cm femur is 157.5 cm.
You Try! The table shows the amount of fruit used to make a smoothie (in ounces) and the total cost (in dollars) of the smoothie. Do the data show a linear relationship? If so, write an equation of a line of fit and use it to estimate the total cost of a smoothie that is made using 8 ounces of fruit.
7 6 5 4 Total cost 3 2 1 0 0 2 4 6 8 10 12 Fruit in a smoothie (ounces)
What I did Points: (2.2, 2.1) and (4.2, 3.1) ? =3.1 2.1 4.2 2.2=1 2 ? 2.1 = 0.5 ? 2.2 ? 2.1 = 0.5? 1.1 ? = 0.5? + 1 Total cost for 8 ounces ? = 0.5 8 + 1 ? = 5 So about $5.00
Homework Textbook page 27 #13, 15, 16
