# Self Study on Simple Linear Regression (Not So Simple Afterall)

I have been practicing some simple linear regression exercises lately and have been deeply challenged by the following question. While the part (A) is something I can concur, the proceeding parts baffled me in many ways.

In general, what I am challenged with is the (Value, Value) expressions.

Appreciate if I will be able to be enlighten by what (B) means and shed some light on the rationale behind the provided answer, so that I may move on to the other parts.

Thank you so much once again

Question

Data Background

This is to answer your question (b). I'm assuming you know what a hypothesis test is, and this reply will use it to demonstrate how the answer is arrived at.

A p-value that is computed for daily wages has a null hypothesis that the slope of that parameter is equal to 0. What this implies is that daily wages has no relationship to quit rate. (I'm simplifying here only for simple linear regression and not multiple regression.)

If you find your p-value to be less than 0.05, it means that this hypothesis has a very small chance of being true or accepted. So we would conclude that the null is to be rejected and daily wages has a non-zero slope, hence a relationship to quit rate.

In the answer, they've given you the values of the upper and lower limits of your 95% confidence interval to be -.43 and -.21. This does not include zero, which means for at least 95% of your cases the value of the slope is non-zero - implying the existence of a relationship.

This however will not be able to tell you if the relationship is strong or weak, that would require the interpretation of r-sqaure.

The good news: You are already able to calculate the regression coefficients, for example you are able to say "per extra year of schooling, the subjects earn on average 1000€ more".

The bad news: You don't understand what a confidence interval is. You need to express how certain you are on your calculation. Imagine you run the experiment with 10 subjects, or with 1000 of subjects. In the second case you are more certain of the effect.

The certainty is expressed with a confidence interval. You say for example "per extra year of schooling, the subjects earn on average 1000€ [750€ to 1250€] more", which mean that you expect to find in 95% of experiments with a fixed number of subjects the coefficients between the confidence interval expressed between brackets.

More can be found in every textbook. Hope this helps.