How do I interpret the output of linear regression model in R?
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