2. Wednesday: Need a graphing calculator today. Need a graphing calculator today.

3. Linear Regression

4. Objectives I can use Linear Regression with a calculator to find Prediction Equations I can use Linear Regression with a calculator to find Prediction Equations I can use Prediction Equations to make other predictions about the data I can use Prediction Equations to make other predictions about the data

5. Regressions You can find a linear regression equation to match your data and then use that equation to make predictions. You can find a linear regression equation to match your data and then use that equation to make predictions.

6. Correlation Co-efficient The correlation co-efficient “r” tells how linear the data is. The correlation co-efficient “r” tells how linear the data is. Values of 1 or –1 indicate perfect linear lines, either positive or negative Values of 1 or –1 indicate perfect linear lines, either positive or negative Values closer to zero mean the data has no linear relationship Values closer to zero mean the data has no linear relationship See next slide for data examples See next slide for data examples

7. 1.0.85 Sample “r Values -.57.17

8. Linear Regressions on the calculator: Turn Diagnostics On. 2nd catalog, arrow to diagnostic on, enter, enter (you should clear the calculator before beginning) 2 nd, +, 7, 1, 2 #1. Go to y = and clear any equations in the calculator. #2.

9. Turn on the scatter plot #3. 2nd y=, 1: enter, arrow to “on” enter, arrow down to “type” and highlight scatter graph (1 st box) enter, arrow to “mark” and highlight 1 st box enter 2 nd Quit

10. Plotting Data When the data you plot forms a near linear relationship, then we can use a linear equation to approximate the graph. When the data you plot forms a near linear relationship, then we can use a linear equation to approximate the graph. We use what’s called a Best-Fit Line. This line is drawn to be as close to the data points as possible, but may not touch them all. We use what’s called a Best-Fit Line. This line is drawn to be as close to the data points as possible, but may not touch them all.

11. Graphing X-axis is the Independent Variable X-axis is the Independent Variable Y-axis is the Dependent Variable Y-axis is the Dependent Variable Common x-axis variables Common x-axis variables –Dates: Years, Months, Days, etc –Time: Hours, Minutes, Seconds –Age, Experience, etc..

12. Independent vs Dependent Always ask this question before graphing: Always ask this question before graphing: Which variable (parameter) depends on the other one for its value??? Which variable (parameter) depends on the other one for its value??? This will be the one plotted on the y-axis!! This will be the one plotted on the y-axis!!

13. Weeks Experience 47816352967 Speed (wpm) 3345492040303822524442 12634578910 20 15 10 5 35 25 30 40 45 x-axis y-axis 0

14. Using the Calculator (Linear Regression) The calculator is a great resource to give us a prediction equation. The calculator is a great resource to give us a prediction equation. It is more accurate than doing the equation Manually It is more accurate than doing the equation Manually We will enter the data into the STAT mode of the calculator We will enter the data into the STAT mode of the calculator X-values go into list L1 X-values go into list L1 Y-Values go into list L2 Y-Values go into list L2

15. Linear Regression Finding the equation of your “Best Fit Line” Finding the equation of your “Best Fit Line” STAT, then EDIT STAT, then EDIT Enter X-Values in L1, Y-Values in L2 Enter X-Values in L1, Y-Values in L2 STAT, then CALC STAT, then CALC Choose (4) LIN REG Choose (4) LIN REG

16. Weeks Experience 47816352967 Speed (wpm) 3345492040303822524442 12634578910 20 15 10 5 35 25 30 40 45 x-axis y-axis 0

17. The table below shows the years of experience for eight technicians at Lewis Techomatic and the hourly rate of pay each technician earns. Experience in years9431106128 Hourly rate of Pay in dollars 1710 719122015

18. Prediction Equations y = 1.234x + 5.574 y = 1.234x + 5.574 Remember: Remember: X = Experience in Years X = Experience in Years Y = Pay rate in dollars Y = Pay rate in dollars We can use this to predict other values We can use this to predict other values

19. When Dealing with Years Must modify years starting at “0” Must modify years starting at “0” If you don’t you get a really negative y- intercept value that won’t match the graph If you don’t you get a really negative y- intercept value that won’t match the graph Example on next slide Example on next slide

20. Inputting Years If the Independent variable is Years and these are your values If the Independent variable is Years and these are your values 1901 1901 1903 1903 1905 1905 1910 1910 1913 1913 1920 1920 Then these are the values we will actually enter for L1 Then these are the values we will actually enter for L1 0 2 4 9 12 12 19 19

21. YEAR MILLIONS OF STUDENTS 190010.6 191012.6 192016.2 1930 21.3 194022.0 195022.3 196032.5 197042.5 198038.2 199038.0 Years must be converted to a number. Let 1900 = year 0, 1910 = year 10, etc

22. Homework WS 3-4 WS 3-4