F09-Diagnostics

F09-Diagnostics - PubH 7405: REGRESSION ANALYSIS SLR:...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
PubH 7405: REGRESSION ANALYSIS SLR: GRAPHICAL DIAGNOSTICS
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
) , 0 ( 2 1 0   N x Y : Model Regression Error Normal   Y. even - E(Y) and , σ , 1 β , 0 β : parameters basic" " the concerning inferences draw to ) y , (x : data" observed " the use We 2 n 1 i i i
Background image of page 2
IMPORTANT QUESTION Do data at hand fit the Normal Error Regression Model ?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Subsequent more important questions: (1) Does it matter if it data do not fit the model or certain part of the model? (the Normal Error Regression Model has more than one parts) (2) If data do not fit certain part of the model – and that could negatively affect the result, could we do something to make them fit? Do we have to pay a price for it?
Background image of page 4
In doing statistical analyses, a “ statistical model ”– such as the “normal error regression model”- is absolutely necessary . For example, the method of least squares give us point estimates but we cannot determine their standard errors without some assumption on the distribution of the error terms. However, a “ model is just an assumption or a set of assumptions ; they may or may not fit the observed data. Certain part or parts of a model may be violated and, as a consequence, the results may not be valid – if the method is not “ robust ”.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
POSSIBLE DEPARTURES FROM THE NORMAL REGRESSION MODEL The regression function is not linear Variance (of error terms) is not constant Model fits all but a few “ outliers Responses (at least some) are not independent Responses terms are not normally distributed Another important predictor (it’s “third factor” – other than X or Y) has been omitted .
Background image of page 6
Besides the data values for the dependent and independent variables, diagnostics would be based on the “residuals” ( errors of individual fitted values ) and some of their transformed values. These residuals are not independent because they are subject to two some constraints as follows: MSE e Y e x e e e x b b Y Y Y e i i i i i i i i i i i 2 ^ _ 1 0 ^ (4) 0 (3) 0 (2) 0 0 (1)
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The errors, or “residuals”, are averaged to zero, not correlated to Predictor values, and not correlated to Responses.
Background image of page 8
SEMI-STUDENTIZED RESIDUALS MSE e MSE e e e i i i _ * If MSE were an estimate of the standard deviation of the residual e, we would call e* a studentized (or standardized) residual. However, the standard deviation of the residual is complicated and varies for different residuals, and MSE is only an approximation. Therefore, e* is call a semi -studentized residual ”.  zero mean with sample a is e ) , 0 ( i 2  N
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Diagnostics could be informal using plots/graphs or could be based on formal application of statistical tests; graphical method is more popular and, most of the times, would be sufficient .
Background image of page 10
PLOTS OF RESIDUALS Plot of residuals against predictor Plot of absolute/squared residuals against predictor
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 42

F09-Diagnostics - PubH 7405: REGRESSION ANALYSIS SLR:...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online