Summary
Summary Research Methods - Data Analysis I
- Course
- Institution
Summary of 2 pages for the course Research Methods In Psychology at UT
[Show more]
Seller
Followkayleighdebruin1
Reviews received
Content preview
RM | Unit 140 - Multiple Linear RegressionBook: Analysing Data Using Linear Models
Chapter 4: 4.15, 4.16, 4.17
Chapter 4.15: Multiple regression in R
Check the book on how to do this in R.
Chapter 4.16: Multicollinearity
In general, if you add independent variables to a regression equation, the proportion explained variance,
R2, increases. Suppose you have the following three regression equations: weight = b0 + b1 × volume + e
(4.39) weight = b0 + b1 × area + e (4.40) weight = b0 + b1 × volume + b2 × area + e (4.41) 136 If we
carry out these three analyses, we obtain an R2 of 0.8026346 if we only use volume as predictor, and an
R2 of 0.1268163 if we only use area as predictor.
→ If we carry out these three analyses, we obtain an R2 of 0.8026346 if we only use volume
as a predictor, and an R2 of 0.1268163 if we only use the area as a predictor. So perhaps you’d think
that if we take both volume and area as predictors in the model, we
would get an R2 of 0.8026346+ 0.1268163 = 0.9294509. However,
if we carry out the multiple regression with volume and area, we
obtain an R2 of 0.9284738, which is slightly less! This is not a
rounding error but results from the fact that there is a correlation
between the volume of a book and the area of a book. Here it is a
tiny correlation of 0.002, but nevertheless, it affects the proportion
of variance explained when you use both these variables.
→ Let’s look at what happens when independent variables are strongly correlated. (See
picture)
→ When two predictor variables are perfectly correlated, either 1 or -1, regression is no
longer possible, the software stops and you get a warning. We call such situation multicollinearity.
But also if the correlation is close to 1 or -1, you should be very careful interpreting the regression
parameters. If this happens, try to find out what variables are highly correlated, and select the variable
that makes the most sense.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller kayleighdebruin1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.21. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
52510 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now