Linear Regression

Regression Consider the following 10 data pairs comparing the yield of an experiment to the temperature at which the experiment was run.

Plot Yield vs Temperature

Clearly yield is dependent on the temperature run.

Regression Model } e i

Regression Model Our job is to find the best estimate a for the true but unknown parameter  and the best estimate b for the true but unknown parameter .

Regression Model Now whatever line we make, for any given point I, we will miss by amount. So how do we find the best line. } e i

Regression Model Two ideas –Minimize the sum of the errors

Regression Model Two ideas –Minimize the sum of the errors All three lines yield a sum of errors equal to 0.

Regression Model Second idea –Minimize the sum of squared errors

Sum of Squared Errors So I have an equation and two parameters to estimate. How do I do that so as to minimize SSE?

Calculus Review How do we find the minimum of this curve? y x

Estimating a Do the same here, take the derivative w/respect to x and set it equal to zero

Estimating b

Estimating a and b

Regression in Excel Set up the Analysis Add- in Toolpak; click on File/options/addins Click on Analysis Toolpak With Analysis Toolpak Highlighted, click on Go

Regression in Excel Add In dialogue box opens With Analysis ToolPak Selected, click ok

Regression in Excel You should now be able to see the Data Analysis ToolPak Click on the Data tab, look for data analysis on the right Scroll down and click on Regression in the data analysis dialogue box

Enter Appropriate cells for y, x, output

Excel Results