Linear VS Non-Linear

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 ….

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.

Linear Regression Model

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.

scatterplot

line of best fit

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

Y=ax2+bx+c Y=ax3+bx2+cx+d

Quadratic Regression Cubic Regression

Y=ax4+bx3+cx2+dx+c Y=axb

Quartic Regression Power Regression

Y=kax Y=klogax

Exponential Regression

Logarithmic Regression

Logistic Regression

)(1

1bXae

y

X Y X 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 1226.58

Step One: Press STATStep Two: Select EDITStep Three: Enter the data

Step Four: Press STAT PLOTStep Five: Select 1Step Six: Select ON

Step Seven: Press WINDOWStep Eight: Adjust x-min, x-max, y-min, and y-maxStep Nine: Press GRAPH

Step Ten: Press STATStep Eleven: Select CALCStep 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.

Press VARS

Step Fourteen: Press ENTERStep Fifteen: Press GRAPHDoes that look like the graph is best fit with a line?

X Y X 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 1226.58

The best regression equation for this set of data is 637.16180707.553057. 2 xxy

X Y

-3 3

-2 -8

-1 -7

0 0

1 7

2 8

3 -3

xxy 81 3