This document discusses regression analysis and its assumptions. Regression can be used to determine if one or more independent variables (IVs) can predict a dependent variable (DV). Simple regression looks at the relationship between one IV and the DV, while multiple regression examines the relationship between multiple IVs and the DV. The key assumptions of regression include linear relationships between variables, no multicollinearity, independence of observations, and normally distributed errors. An example of applying regression to examine the relationship between average daily clicks and direct sales revenue is provided.

1.  Purpose – Determine if one or more IVs
can predict a DV
 Examples:
• Does your height (IV) predict how much money
you will spend (DV)?
• Does the number of store managers predict how
often the machine will break down (DV)?
• Does the number of clicks (IV1) and the number of
comments (IV2) on the blog predict the size of
revenue (DV)?

2. Research Question Inferential Statistics
Compare means of 2 numeric T test
variables
Relate 2 categorical variables Pearson Chi Square
Relate 2 numeric variables Pearson Correlation r
Use 1+ IVs to explain 1 numeric DV Regression

3.  Correlation tells us how X relates to Y (in
the past)
 Simple Regression tells us how X
predicts Y (in the future)
• E.g., Does AvgDailyClicks predict
DirectSalesRevenue?
 Multiple Regression tells us how X1, X2,
X3, ….. predicts Y
• E.g., Do NumberBlogAuthors & AvgDailyClicks
predict SponsorRevenue?

4.  The relationship between Xs and Y are
linear
 If you have 2 or more Xs, they are not
perfectly correlated with each other
 Xs are not correlated with external
variables
 Independence – Any two observations
should be independent from each other.
 Errors are normally distributed
 And a few others

5.  Example:Does Number of Stupid
Customers predict Self Checkout Error
Rate?
 When we use X to predict Y:
• X = the predictor = the independent variable (IV)
• Y = the predicted value = the dependent variable (the
value of Y depends on the predictor X) (DV)
• You’re basically building a linear model between X and
Y:
Y = Constant + B*X + error

6.  Y = Constant + B*X + error
 Y= 1 + 2*X
Constant = 1
Slope B = 2
Source: wikepedia

7. Who is the best fitting model?
(Hint: Not Kate Moss)
Line that’s closest to all dots

8. Goodness of Fit (R2):
How well does the line fit the data?
(How well does Kate fit the average woman?)
(constant)
Slope B
Distances to regression line = error
Good fit = small errors

10.  Y = Constant + B*X + error
 DirectSalesRevenue = 19.466-.003*AvgDailyClicks+error
Constant is significantly greater than zero
Slope (-.003) is significantly less than zero
Goodness of Fit (R2): Model explains 59% variations in DirectSalesRevenue

11. The number of average daily clicks
significantly predicted direct sales revenue, b
= -.03, t(39) = 14.72, p < .001. The number of
average daily clicks also explained a
significant proportion of variance in direct
sales revenue, R2 = .59, F(1, 38) = 42.64, p <
.001. These findings suggest that, websites
with more average daily clicks tend to have
lower direct sales revenue level.

12. Y=200X (R2 = 45%)
Given any X, we can predict value of Y with 45% accuracy

13.  Assumptions: Xs are somewhat independent; Y values are
independent; Y values are normally distributed; errors are normally
distributed; X Y relations are linear; no outliers
• Example: Time series data are NOT independent – stock price today depends on
stock price yesterday which depends on stock price the day before, etc.
 Multiple regression is just an extension of single regression
• Use multiple Xs (e.g., both AvgDailyClicks and NumberAuthors) to
predict Y
• When you have a condition (e.g., customer choice depends on gender;
brand awareness depends on comm. channel; number of applications
depends on program of study), you need to create an interaction term 
next class
 When an X is categorical (e.g., whether the blog host is Google or
WordPress): Code X in numbers – e.g., 0 is Google, 1 is WordPress
 When Y is categorical (e.g., whether the blog won the Outstanding
Blog Award): Code Y in numbers – e.g. 0 is No, 1 is Yes, and use
Logistic Regression

14.  What is your Y (the value you want to predict)?
 Is your Y categorical?  Do you need Logistic Regression?
See the instructor for help
 What is your X (your predictor variable)? How many Xs do
you have?
 Is any of your Xs categorical?  Do you have a coding
scheme?
 Do you have a condition? (e.g., customer choice depends
on gender; brand awareness depends on comm. channel;
number of applications depends on program of study) 
See the instructor for help

15. Research Question Inferential Statistics
Compare means of 2 numeric variables T test
Relate 2 numeric variables Pearson Correlation r
Relate 2 categorical variables Pearson Chi Square
Use 1+ IVs to explain 1 numeric DV Regression