Class Notes (834,967)
United States (323,999)
Statistics (75)
STAT 301 (55)
Lecture

Simple linear regression model, verifying assumptions

3 Pages
97 Views
Unlock Document

Department
Statistics
Course
STAT 301
Professor
Brett Hunter
Semester
Fall

Description
14 November The Simple Linear Regression Model When conducting a regression analysis on an explanatory variable and a response variable, the following population model is assumed Y = β 0 β x1+ ε β0is the population y-intercept β1is the population slope 2 ε are random errors, where ε ~ N (0, σ ) Without ε, all observed points would fall on the regression line My = β 0 β x 1 Mean of response variable Assumptions in the model The distribution of ε at any particular X value has mean 0. The distribution of ε at any particular X value is normal. The variance of ε, denoted σ , is the same for any particular X value. ε is homoscedastic The random observations ε , ε ,1… 2 assocnated with different observations are independent of each other. We can sum up these assumptions as iid 2 εi N (0, σ ), i = 1, …., n iid = independently and identically distributed In order to perform a regression analysis, we need to avoid any serious violations of the assumptions. We check these assumptions graphically. y Recall that e = i - i i are residuals/errors for our fitted model. We can standardize our residuals ei di= esimateds.d.of e i
More Less

Related notes for STAT 301

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit