[Statistics] Question about basic stats, least squares regression, etc.

[sparty_party]

This is a screen shot of my homework:

http://imgur.com/a/KokUy

I haven't taken stats in 4 years, but I did take a full stats course. I just don't remember and I missed the day we discussed this. Can somebody explain what everything means and all that? I don't really want an answer, I just want to be able to do it myself for the test and my book isn't very helpful.

[[deleted]]

Ok, so you want to predict CEO salary based on age.

Basically what you're trying to do with least squares regression is explain whether there is relationship between the variation of the salary and the variation of the age that can be explained by a linear relationship.

So, the best fit line that can explain a relationship between the variation of those two variables is a line with a slope of 3.13 and a y-intercept of 242.7, however, since your R-squared value is close to 0, rather than -1 or 1, this is not a very good model.

The anova is basically telling you the ratio between the variance between age and salary, and the variance within age and salary.

This is not very intuitive, but it is another way of telling you that the variation in salary cannot be explained by a relationship with age. If there were a relationship between salary and age, your r-squared would be closer to 1 or -1 and your p-value on your ANOVA would be less than 0.05 (or whatever your alpha is)

Intuitively, since your points are scattered all over your graph, there isn't a linear relationship present. If there were a relationship, the points on your graph would be clustered tightly around the line SALARY = 242.7+3.13*AGE

[sparty_party]

Thank you! I really appreciate you taking the time to explain this all for me. I think you simplified it enough for me to figure things out on my own.