Statistics Correlation https://www.123rf.com/photo_6622261_statistics-and-analysis-of-data-as-background.html

Inputs and Outputs In formulas, some variables are “input” variables The thing you are calculating with the formula is the “output”

Inputs and Outputs In a factory, the inputs are the components

Inputs and Outputs The output is the final product

Inputs and Outputs The input variable is ALWAYS put on the x-axis (horizontal axis) No reason – it’s a TRADITION!

Inputs and Outputs It can sometimes be hard to figure out which is the input variable and which the output variable

Inputs and Outputs Input variables sometimes CAUSE the result

Inputs and Outputs Sometimes input variables occur before the out variables

Inputs and Outputs Frequently the input variables cannot be controlled by us (time, for example) For this reason, input variables are frequently called “independent” variables

Inputs and Outputs And, the output variables (which depend on the values of the independent input variables) are called “dependent” variables

Questions?

Correlation A relationship can be seen by graphing the independent and dependent variables in a scatter graph

Correlation A linear relationship is very common

Correlation When we calculated a correlation coefficient, we said it was a measure of the closeness to a linear relationship between the two variables

Line of Best Fit That means, we could find the formula for a line that would be the best fit for the two variables

Line of Best Fit We “fit” a line to the data

Line of Best Fit Real-world data rarely lands exactly on a straight line

Line of Best Fit But we fit the “best” line to the data

Line of Best Fit When you graph two variables on an x-y plot, you can fit a line through the data called a “trend line”

Line of Best Fit This trend line is a “line of best fit” to the data

Regression The “line of best fit” is created by minimizing the total distance of all the points to the line (deviations)

Regression The line of best fit is called the “regression” line

Regression Because it is a line, it has an equation: y = b + mx m = slope b = y-intercept

Regression The slope “m” and the correlation coefficient “r” will both have the same sign

Regression R2 tells how closely the regression line “fits” the data – “goodness of fit”

Regression As you can imagine, the calculations for correlation and the regression line are scary

Regression Hooray for Excel!

Regression Francis Galton

Questions?

Regression in Excel Does coming to class affect my grade?

What Does It Say?

Regression in Excel Edwin Hubble gathered and analyzed data from astronomical objects He used regression to show that the universe is expanding http://www.thefamouspeople.com/profiles/images/edwin-powell-hubble-1.jpg

Regression in Excel Let’s take a look!

Regression in Excel What do we do first?

Regression in Excel What do we do first? GRAPH THE DATA!

Regression in Excel

Regression in Excel Does it look like a straight line would fit the data well?

Regression in Excel Now we’re going to go to: Data Data Analysis Regression

Regression in Excel They want “y” first (I HATE this…)

Regression in Excel Let’s use “distance” for “x” and “velocity” for “y”

Regression in Excel Eeek! What’s all this????

Regression in Excel Here’s the RSQ. What is the %?

Regression in Excel For the trend line, you need:

Regression in Excel This (believe it or not) is the equation of the line of best fit!

Regression in Excel Line of best fit: y = mx + b

Regression in Excel Our equation is: Vel = 505.8409 x Dist + -48.3429

Regression in Excel Highlight and copy:

Regression in Excel Paste on the “Hubble” page

Regression in Excel Add a new column heading: Trend

We’re going to calculate our line:

Copy it down…

Oops! That doesn’t look right!

The reference cells are changing for each row We need to make those constant

Go back to the first entry Add a $ before the row numbers you want to keep constant

Now, copy it down!

Much better!

Regression in Excel Create a new graph:

Regression in Excel Make it purty! To make the trend line a line: change Marker Options to “none” change line color to “solid line”

TAH-DAH!

What Does It Say?

Regression Note: some people use the symbol “ŷ” for the trend data corresponding to the “y” observation data

Regression in Excel Summary of Regression Analysis: Data/Data Analysis/Regression Enter “y” first Copy the first two coefficients in the bottom table Trend line is: =Coeff*Data+Intercept Make a graph Change the trend dots into a line

Questions?