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I have the following linear regression model and its analysis. There are a few errors, but I am not very sure about the errors. I have not succeeded in finding them so far.
First, the 95% confidence interval for the slope should be
So the calculation is wrong.
Second, I'm not sure about the interpretation of the confidence interval. How would you interpret it in the context ?
So, the question is centred around the meaning behind a confidence interval.
The main principle behind confidence intervals is the following:
It is very costly and time-inefficient (if not impossible) to sample the whole population (i.e. all UCLA students from China and Hong Kong) and measure their cultural adjustment. Therefore, we can take a sample from this population (i.e. 200 students).
From this sample we can then develop a linear model between input features (i.e. country) and the level of cultural adjustment and establish the slope of the model.
The slope alone only tells us the slope for the linear model trained on these 200 students. We want to have an estimate of the slope that we have at least 95% confidence that it lies in a particular range. Hence, confidence intervals.
Here is an article on confidence intervals for further reference: https://www.simplypsychology.org/confidence-interval.html
For me the main point to look at here is the adjusted R² of 0.02 which basically tells us that the country of origin alone is not a great predictor of cultural adjustment and that we cannot derive any practical conclusions.
Seeing as potentially important control variables or other predictors have not been included in the model we cannot be sure for example that gender, years spent in the US (prior to test), income / social status of parents, etc. do not play a heavy role or influence the result.
So practically the interpretation would be that the model isn't conclusive and more work needs to be done.
Depending on the scale of "cultural adjustment" the confidence interval supports this interpretation basically telling us that a student from Hong Kong is likely to score the same or much better than a mainland Chinese student, which is to say,the model isn't confident at all (unless the scale is 1-100 or higher in which case the model would be confident in seeing no differences).
The computation of observed confidence interval is incorrect showing a minus sign. Therefore, you can not interpret the confidence interval regarding the difference in the students of two countries.
Further, expected confidence interval has been defined incorrectly. It should be Beta = b + or - (minus) 1.96 × S. E.
It is noticeable that the computed t is more than the table value of t =1.96 at 5%.This implies thar there is a significant difference between Hongkong and mainland Chinese students with regard to cultural adjustment.
