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--- rem4:t-tests_and_linear_models [2008/10/22 15:05] – thorisson
+++ rem4:t-tests_and_linear_models [2024/04/29 13:33] (current) – external edit 127.0.0.1
@@ Line 19: / Line 19: @@
 | Sample  | 20 individual fish are tested.   |
 | Variables  | Dependent: Health.  Independent: Oceanic area (N,S).  Dependent variable is measured with the "famous Health Probe".  |
-| Subject pool  | N=20; random sample.  |
+| Subject pool  | N=20; random sample. Specify by which means/method the randomness is generated and followed.  |
 | Gathering data  | Repeated measures: 20 measurements for indexes of health: \\ North:97,99,88,77,99,20,87,88,89,65; \\ South:66,48, ....   |
 | **What we have so far**  | Basically, we have a bunch of measurements which came from two different parts of the country. They will probably have a different mean, median, etc. -- it's unlikely that they will be equal. This difference, we would like to find out -- is it a true representation of the actual fish population in each of these two different locations?  |
@@ Line 62: / Line 62: @@
 | How do we find the line?  | Least Squares Criterion: We select the linear function that will yield the smallest sum of squared residuals  |
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 ===Linear Correlation===
 | Given a linear function  | Given an X-score, the predicted Y-score is given by the line. However, in reality the Y-score rarely falls straight on the line.   |
-| Need estimate of error  | We must estimate how closely real Ys follow the predicted Ys  |
+| Need estimate of error  | We must estimate how closely real Ys (Y) follow the predicted Ys (Y')  |
-| The measure most commonly used  | Standard Error of Estimate: How far, on average, real Ys fall from the line  |
+| The measure most commonly used  | Standard Error of Estimate  |
-| Formula for Std. Err. of Est. | SQRT( (SUM(Y' - Y)^2 ) ) / N)  |
+| Formula for Std. Err. of Est. | http://cs.gmu.edu/cne/modules/dau/stat/regression/multregsn/mreg_2_frm.html   |
+| What it tells us  | How far, on average, real Ys fall from the line  |
+| The smaller the Std. Err. of Est. is ... | ... the better a predictor the line is  |
+| Main limitation of linear models  | Assumes -- apriori! -- a linear relationship  |
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