[統計]Regression modelling(急!!)

1.我的想法對嗎?
Yes, the SD information is used when carrying out hypothesis test checking if the intercept (for the constant term) and slope (for the predictor term) are significantly different from zero.

2.我老細又對嗎?
Partly. The SD of a regression line can be used to generate "confidence interval of regression line" which are two lines, one above, one below the regression line that look like an hourglass (see links below for example).

By default the confidence interval band is 95%. This just means that "if you carry out the regression test 100 times, about 95 of them will lie inside this boundary." So, your boss is both right and wrong. Higher SD does mean we are less sure how the real population regression line look like (cause the 95% confidence interval band will be so wide); however, it's not your sample beta that fluctutes. Your sample is your sample and once you collected and ran a regression, the beta is the beta you get form SPSS/SAS, it does not fluctuate. What "fluctuate" (or to be more precise, "is difficult to be estimated") is the real regression slope.

3.可否幫小弟找找相關supportive document..?
If you open any statistics book to the chapter of regression and look for "confidence interval", you should be able to get the reference. This is not new thing, so could be quite difficult to get current journal article.

http://www.vias.org/tmdatanaleng/cc_regress_confidiv.html
http://www.tufts.edu/~gdallal/slr.htm

2007-12-16 06:46:58 補充：
Q1: Yes, different samples, but drawn from the same population.Q2: High means bigger in magnitude. If SE is big, CI is also wider & the CI band will be farther away, which means we are less sure what the true slope is.

2007-12-16 06:47:19 補充：
Q3: If the variable fulfill normality, then yes, you can test with z- or t-test. The p-value (or sig. in SPSS) is given at the end of the regression output.

Really thx for 天火雷answering!!
Another questions comes from your ans.


"if you carry out the regression test 100 times, about 95 of them will lie inside this boundary" ( About CI)
Firstly a simple question, do you mean carrying out reg test with different samples in 100 times?(becoz the same sample will give same answer..)

" Higher SD does mean we are less sure how the real population regression line look like (cause the 95% confidence interval band will be so wide)"
What's the definition on "high"?
Can I use normal distribution to explain the acceptance of sd?
(My boss ask me to find what value of sd that we can accept beta to become accurate...?)

天火雷gives victor_ally really good points on sd.(sample is sample!)
Grateful to see the answers