There are many tutorials on regression on YouTube, some better than others. I am providing links to some that you may find helpful. Again, I am most interested in practical solutions using Excel since that is a program you should all have.

- Basic calculation of correlation coefficient r in Excel: http://www.youtube.com/watch?v=yD_yIAnSnTE (both manually and using Excel functions).
- Basic fitting line to data http://www.khanacademy.org/math/probability/regression/regression-correlation/v/fitting-a-line-to-data
- Khan has a good discussion of why correlation is not necessarily causation (I think this is linked in BB)
**Good for Module 7 Discussion 2:**http://www.khanacademy.org/math/probability/regression/regression-correlation/v/correlation-and-causality **Excellent**discussion of the complete Excel simple regression output (looking at the relationship between Amazon’s stock price and the S&P 500 index) including residuals: http://www.youtube.com/watch?v=c5blVUkkjTM- This is a 15 minute video concentrating on the nuts and bolts of simple regression done well, but the main reason I include this link is the last 4 minutes really do a good job of explaining the difference in e (estimated error) and Ɛ (theoretical error from the theoretical real equation): http://www.youtube.com/watch?v=aq8VU5KLmkY
- This is an
**Excellent**, detailed discussion of degrees of freedom, r-square and adjusted r-square.**Must see**: http://www.youtube.com/watch?v=4otEcA3gjLk - This is an
**Excellent**presentation of how to make predictions using Excel multiple regression output including construction of confidence intervals**(Important):**ProTDub YouTube channel http://www.youtube.com/watch?v=E73AJ73-S6g **ProTDub**video 2 on checking the independence assumption by checking residuals in Excel multiple regression: https://www.youtube.com/watch?v=B5PtHcsoL9c**ProTDub**video 3 on checking the constant variance assumption by checking residuals from an Excel multiple regression: https://www.youtube.com/watch?v=4zQkJw73U6I***This tutorial shows how to calculate the beta for a stock using regression as well as the slope method.****http://www.youtube.com/watch?v=7LiK-qbmPsw**

I have reviewed the series of tutorials produced by Dr. Jason Delaney of Georgia Gwinnett College on youTube. They primarily illustrate how to do the math using Excel but there are also a few theoretical ones that are very good. I recommend these as a solid, practical take on multiple regression for students. I include Dr. Delaney’s description of each video in italics. It was my original intention to produce a series on Excel 2013 myself but why reinvent the wheel? Note: I brought them all here because I could not find a YouTube channel for him that had all these in one place. The ones with an asterisk are helpful for the final extra credit problem.

***Multiple Regression 1-Intro to Regression – Jason Delaney (22 min)**https://www.youtube.com/watch?v=eLpfEml4Vak*This video us moves from simple linear regression to multiple regression. I discuss the differences introduced by increasing the number of regressors, and we cover:**– the multiple regression model**– the regression equation and estimated regression equation**– the least-squares approach**– the SST, SSE, and SSR**– the R-squared and adjusted R-squared****Multiple Regression 2 – (F test and t test) (12 min) – Jason Delaney**https://www.youtube.com/watch?v=DhMIfq9CKeg*This video covers standard statistical tests for multiple regression. I cover:**– assumptions placed on the error term**– the F test of overall or joint significance**– hypotheses**– F test statistic**– p-value and its interpretation**– the t test of individual significance***Multiple Regression – F test for adding variables – 16.12 – LPG (13 min) Jason Delaney:**https://www.youtube.com/watch?v=9mg5vHFIFRE*This video presents a walk-through solution for a problem illustrating the use of an F test to determine if additional variables contribute significantly in a multiple regression model.*****Multiple Regression 3 – presentation on dummy variables and interactions (25 min) by Jason Delaney:**https://www.youtube.com/watch?v=MAsZVPh0F-c*This video introduces the use of dummy variables for regression modeling with categorical or qualitative data. Dummy variables are frickin amazing. I cover:**– the basics of dummy variables**– an example using apartment rents in two cities**– omitted variable bias**– constructing dummy variables**– estimating coefficients on dummy variables**– interpreting those coefficients as shifts in the intercept**– dummy variables with more than 2 categories****Excellent, though 30 min long, presentation of how to model a multiple regression with dummy (categorical) variables in Excel -Jason Delaney:**https://www.youtube.com/watch?v=H07l1zgM-cw*In this video, I present an example of a multiple regression analysis of website visit duration data using both quantitative and qualitative variables. Variables used include gender, browser, mobile/non-mobile, and years of education. Gender and mobile each require a single dummy variable, while browser requires several dummy variables. I also present models that include interactions between the dummy variables and years of education to analyze intercept effects, slope effects, and fully interacted models. In short, I cover:**– multiple category qualitative variables**– dummy variables**– intercept effects**– slope effects**– dummy interactions*****Regression by Jason Delaney re dummy variables –restaurant example (13 min):**https://www.youtube.com/watch?v=STk7n9VsjYg*This video walks through a practice problem illustrating the use of dummy variables for regression modeling with categorical or qualitative data. Dummy variables are frickin amazing. I cover:**– the basics of dummy variables**– an example using types of restaurants**– constructing dummy variables**– estimating coefficients on dummy variables**– interpreting those coefficients as shifts in the intercept****Regression 4 by Jason D – understanding Excel regression output (27 min)**https://www.youtube.com/watch?v=Ut22-WLvEVw*This is probably the most important video in this series. I very methodically introduce five stories of posited mathematical relationships, how to translate them into mathematics via regression modeling, and how to interpret the results from regression estimation.***Multiple Regression 5 –F test for a subset of variables (15 min) – Jason Delaney***https://www.youtube.com/watch?v=g7X4k_ioxk4**Heretofore, we kind of had to eyeball the differences between models to choose which was better. In this video, I discuss a statistical test to see if additional regressors improve the regression estimates in a statistically significant way. I cover:**– examples of when this might be useful**– the intuition behind the test**– the two models being compared**– the hypotheses**– the test statistic**– finding and interpreting the p-value***Multiple Regression – Estimated regression equation practice problem – 15.07 (13 min) Jason Delaney**https://www.youtube.com/watch?v=88n87Hv-R_s*A guide to solving Anderson Sweeney & Williams 11e Chapter 15 Problem 7, using Microsoft Excel. The dataset is titled “Laptop.xlsx”.***Multiple Regression 6 – Jason D – Residual plots (22 min):**https://www.youtube.com/watch?v=wtT4zkxNy-A*We have made some strong assumptions about the properties of the error term. In particular, we have assumed our linear fit is appropriate and that our errors have equal variance (homoskedasticity). We can plot the residuals to see if these are violated. I cover:**– residual plots – model misspecification**– omitted variables – curvilinear relations – heteroskedasticity (non-constant variance) – transforming the dependent variable – logarithmic and reciprocal transformations***Multiple regression – Residual plots and dependent variable transformations – 16.7 Lightrail – (14 min) Jason Delaney**https://www.youtube.com/watch?v=7UcpceEBlKE*This video walks through a practice problem illustrating the use of residual plots for regression modeling and dependent variable transformations to correct for heteroskedasticity. I cover: – residual plots – model misspecification – heteroskedasticity (non-constant variance) – transforming the dependent variable – logarithmic and reciprocal transformations***Multiple Regression 7 – Nonlinear (curvilinear) relationships****(19 min)-Jason Delaney:**https://www.youtube.com/watch?v=9J3PZsngAeY In all the regression models thus far we have been assuming linearity. Regression methods actually find uses in many non-linear applications. In this video I discuss: – the general linear model – interaction effects – quadratic relationships – growth models – estimating the Cobb-Douglas output elasticities – estimating fixed costs and unit costs

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