2. 2 Excel* MegaStat Minitab SPSS JMP POM *We will focus on this readily available software in the demonstrations to follow Statistical Software

3. 3 Regression lines are typically used when you want to predict possible future values for variables Regressions can be both linear and non-linear; we will focus on linear You can have an n-dimensional regression line, which means you can have several independent variables effecting the dependent variable When do I need a Regression Analysis?

4. 4 Let’s look at an example: Suppose you collect data on Domestic Revenue in Freight Ton Miles for Non Scheduled Cargo flights. This data is available on the FAA webpage: http://apps.bts.gov/xml/air_traffic/src/datadisp.xml You can easily download this data in an Excel Format from this website. Refresher: Simple Linear Regression Two variables: One independent (x) and one dependent (y) y=β 1 x+β 0 Β 1 is called the slope and β 0 is called the y-intercept

5. 5 Multiple Linear Regression Question: Can we use air carrier delay, weather delay, and arrival delay to predict security delays?

6. 6 Multiple Linear Regression Take a look at the data in the attached Excel File under the data Tab. To make this easy, we just used 202 observations versus the sleuth of data provided (FYI for you only; the FAA is a wonderful source of data)

7. 7 Multiple Linear Regression Let’s perform the analysis using Excel’s Data Analysis tab. If you need to download Excel’s Data Analysis package, see here: http://office.microsoft.com/en-us/excel- help/load-the-analysis-toolpak- HP010021569.aspx http://office.microsoft.com/en-us/excel- help/load-the-analysis-toolpak- HP010021569.aspx

8. 8 Multiple Linear Regression To do a multiple regression, we do just as we did in the simple linear regression except highlight all the independent variables (thus when you organize your data you need all your independent variables in adjacent columns to make the analysis easier).

9. 9 Simple Linear Regression: Data Analysis Step 1: Go to the data tab Step 2: Select Regression Step 3: Click on the square next to y-data and highlight all the data for your dependent variable Step 4: Do the same for the x variables; you would highlight all x data columns. Step 5: Click okay (or make minor changes as you see fit for output, alpha, etc.)

10. 10 Multiple Linear Regression Once you run the regression, see video, what does all this stuff mean? P-values: Which variables actually matter. For this example, they all do as the p-values are all less than 0.05. If we had a p-value greater than 0.05 we would not want to include that variable.

11. 11 Multiple Linear Regression Once you run the regression, see video, what does all this stuff mean? Continued: The equation of the line can be found in the coefficients column: Y=4.531248617+0.001481901x 1 +0.0065020 77x 2 +-0.024438504x 3 Note: Be sure to remember the associate between the x variables and your data: x 1 =arrival delay, x 2 =carrier delay and x 3 =weather delay