Lecture 7 Linear Regression Diagnostics
Lecture 7 Linear Regression Diagnostics
BIOST 515 January 27, 2004
BIOST 515, Lecture 6
Major assumptions
1. The relationship between the outcomes and the predictors is (approximately) linear.
2. The error term has zero mean.
3. The error term has constant variance.
4. The errors are uncorrelated.
5. The errors are normally distributed or we have an adequate sample size to rely on large sample theory.
We should always check fitted models to make sure that these assumptions have not been violated.
BIOST 515, Lecture 6
1
Departures from the underlying assumptions cannot be detected using any of the summary statistics we've examined so far such as the t or F statistics or R2. In fact, tests based on these statistics may lead to incorrect inference since they are based on many of the assumptions above.
BIOST 515, Lecture 6
2
Residual analysis
The diagnostic methods we'll be exploring are based primarily on the residuals. Recall, the residual is defined as
ei = yi - y^i, i = 1, . . . , n,
where
y^ = X^.
If the model is appropriate, it is reasonable to expect the residuals to exhibit properties that agree with the stated assumptions.
BIOST 515, Lecture 6
3
Characteristics of residuals
? The mean of the {ei} is 0:
1n
e? = n
ei = 0.
i=1
? The estimate of the population variance computed from the sample of the n residuals is
S2 =
1
n-p-1
n
e2i
i=1
which is the residual mean square, M SE = SSE/(n-p-1).
BIOST 515, Lecture 6
4
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- logarithmic transformations regression modeling
- glm residuals and diagnostics myweb
- linear regression using stata princeton university
- multiple linear regression mlr handouts
- multiple regression
- lecture 2 linear regression a model for the mean
- 3 2 least squares regressions
- lecture notes 7 residual analysis and multiple
- lecture 7 linear regression diagnostics
- regression finding the equation of the line of best fit
Related searches
- simple linear regression test statistic
- linear regression coefficients significance
- linear regression test statistic calculator
- linear regression without a calculator
- linear regression significance
- linear regression coefficient formula
- linear regression significance test
- linear regression slope significance testing
- linear regression statistical significance
- linear regression hypothesis example
- simple linear regression hypothesis testing
- simple linear regression null hypothesis