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Real Data Analysis Linear VS Non-Linear

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**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 ….

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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.

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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

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**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

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**Nonlinear Regressions**

Quadratic Regression Cubic Regression Y=ax2+bx+c Y=ax3+bx2+cx+d

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**Nonlinear Regressions**

Quartic Regression Power Regression Y=ax4+bx3+cx2+dx+c Y=axb

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**Nonlinear Regressions**

Exponential Regression Logarithmic Regression Y=kax Y=klogax

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**Nonlinear Regressions**

Logistic Regression

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**Calculating a Regression Function**

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 Step One: Press STAT Step Two: Select EDIT Step Three: Enter the data

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**Calculating a Regression Function**

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

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**Calculating a Regression Function**

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

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**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.

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**(How to find the Y-Variables)**

Press VARS

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**Calculating a Regression Function**

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

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**Calculating a Regression Function**

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**Calculating a Regression Function**

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 The best regression equation for this set of data is

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**Practice: Find the Best Fit Equation**

X Y -3 3 -2 -8 -1 -7 1 7 2 8

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Least-Squares Regression Section 3.3. Correlation measures the strength and direction of a linear relationship between two variables. How do we summarize.

Least-Squares Regression Section 3.3. Correlation measures the strength and direction of a linear relationship between two variables. How do we summarize.

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