1. Real Data Analysis
Linear VS Non-Linear

2. Regression http://n-steps. tetratech-ffx
One of the most common statistical modeling tools used, regression is a technique that treats one variable as a function of another.
The result of a regression analysis is an equation that can be used to predict a response from the value of a given predictor.
Regression is often used in experimental tests where … one tests whether there is a significant increase or decrease in the response variable ….

3. What’s that mean?
One tool used in the ‘real world’ to help make business decisions and determine the results of scientific experiments is regression analysis.
You use regression analysis to see if one thing (like the periods of time a store is open) strongly affects another thing (like how much money the store makes).
There are many types of regression analysis.
Two of those are linear and nonlinear.

4. Linear Regression
line of best fit
scatterplot
The relationship between the two variables is directly proportional.
Directly Proportional: If one value increases, the other increases as well.
The function that passes through the middle of the scatterplot is called the line of best fit.
Linear Regression Model

5. Nonlinear Regressions
There are many types of nonlinear regressions due to the fact that they are anything that is not linear.
Quadratic Regression
Cubic Regression
Quartic Regression
Power Regression
Exponential Regression
Logarithmic Regression
Logistic Regression

6. Nonlinear Regressions
Quadratic Regression
Cubic Regression
Y=ax2+bx+c
Y=ax3+bx2+cx+d

7. Nonlinear Regressions
Quartic Regression
Power Regression
Y=ax4+bx3+cx2+dx+c
Y=axb

8. Nonlinear Regressions
Exponential Regression
Logarithmic Regression
Y=kax
Y=klogax

9. Nonlinear Regressions
Logistic Regression

10. Calculating a Regression FunctionX Y 5
119.94 30
424.72 10
166.65 35
591.15 15
213.32 40
757.96 20
256.01 45
963.36 25
406.44 50
Step One: Press STAT
Step Two: Select EDIT
Step Three: Enter the data

11. Calculating a Regression Function
Step Four: Press STAT PLOT
Step Five: Select 1
Step Six: Select ON

12. Calculating a Regression Function
Step Seven: Press WINDOW
Step Eight: Adjust x-min, x-max, y-min, and y-max
Step Nine: Press GRAPH

13. Calculating a Regression Function
Step Ten: Press STAT
Step Eleven: Select CALC
Step Twelve: Select
4: LinReg(ax+b)
[we’re going to see if it’s
linear]
Step Thirteen: Tell the Calculator where you want the equation stored.

14. (How to find the Y-Variables)
Press VARS

15. Calculating a Regression Function
Step Fourteen: Press ENTER
Step Fifteen: Press GRAPH
Does that look like the graph is best fit with a line?

16. Calculating a Regression Function

17. Calculating a Regression FunctionX Y 5
119.94 30
424.72 10
166.65 35
591.15 15
213.32 40
757.96 20
256.01 45
963.36 25
406.44 50
The best regression equation for this set of data is

18. Practice: Find the Best Fit EquationX Y -3 3 -2 -8 -1 -7 1 7 2 8