Hi, I operated linear regression on my sample including 3 groups.
But I feel the estimate is somewhat "generalized" within this three group,
and I want to compare each group's estimate of regression line.
Of course, they showed different estimate value but (if possible,) how can I know whether they are really different, or it is in just "acceptable" variation?
If I understand your question you wish to test if the three group regressions are really the same..
.see the test in the attachment to do that. Good luck to you, David Booth
Hyeji Kang -
So are you saying that you can divide your sample into three separate parts/samples, and you are comparing the linear regressions you obtained in each case? What about the linear regression you obtain with the entire sample?
If you look at prediction intervals around each line, you could see if the others fall within it. I just think it is often good to see some graphics to understand your data and modeling better.
Consider Figure 3 on page 13 in
https://www.researchgate.net/publication/261508465_Use_of_Ratios_for_Estimation_of_Official_Statistics_at_a_Statistical_Agency
It is explained there, but I will also attach the graph here.
You might also look at Penn State info on prediction intervals and confidence intervals for means. Consider
Penn State (2021b). STAT 462: Applied Regression Analysis, 4.11 - Prediction Interval for a New Response. Retrieved from https://online.stat.psu.edu/stat462/node/127/, May 9, 2021.
Do you have any other data for further cross-validation?
Cheers - Jim
Please say what you mean by "really different" and "acceptable variation"?
The questions by James R Knaub and Daniel Wright are mind-blowing. Looking forward to getting insightful answers.
Daniel Wright Sorry, my question was quite ambiguous. I meant the slope of regression line is possible to compare statistically just like ANOVA among several groups. For example if three groups’ slope was 1,1.5,2.0 respectively, can we say they are significantly different and consequently conclude these groups have different tendency between independent variable and dependent variable?
If I understand Hyeji Kang's question, it should be a simple matter of estimating a model that includes the group variable as a factor variable (with df=2), the quantitative (or metric) predictor variable, and the 2-df interaction between them. The F-test for the interaction term tests the null hypothesis that in the 3 populations the groups are sampled from, the slopes are the same. I believe this test addresses Hyeji's question about whether the slopes are really different.
Hyeji, given your response to David's post, I an inclined to think you may have already discovered this approach. But if not, I'm sure readers could point to specific examples if they knew what software you are using. E.g., if I knew you were using Stata, I might direct you to this page:
https://stats.oarc.ucla.edu/stata/faq/how-can-i-understand-a-categorical-by-continuous-interaction-stata-12/
HTH.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Regression