Linear Regression – 25 important questions

There are several questions I want my students to understand and master in this chapter on Linear Regression:

1. What are the four assumptions of linear regression (simple linear and multiple)?
2. What is meant by dependent and independent variables? (y is dependent, x are independents)
3. What is difference between simple linear and multiple linear regressions?
4. What is difference between regression model, and estimated regression equation?
5. What is a residual? How is it computed? (actual y – estimated y)
6. How do you interpret b1 in simple linear regression?
7. How do you interpret b1 in multiple linear regressions?
8. What happens when p value for f test is lower than alpha i.e. what do you conclude?
9. What happens when p value for t test is lower than alpha i.e. what do you conclude?
10. What is the difference between coefficient of determination, and coefficient of correlation?
11. What does coefficient of determination explain? (in terms of variation)
12. What are df associated with f test and t tests for simple linear and multiple linear regressions?
13. How to find f test and t test p values?
14. How to write estimated regression equation from coefficient output?
15. What is adjusted R²?
16. How to compute R²? (R² = SSTR/SST; and also R² is square of R)
17. What are H0/Ha for f test and t tests?
18. When do you reject H0 and when do you fail to reject H0 – for f and t tests?
19. How are SSTR, SSE and SST related? (SST = SSTR + SSE); Also note: in SPSS ANOVA output associated with Regression>> Regression is same as Treatment and Residual is same as Errors.
20. How to find MSTR and MSE from SSTR, SSE and df? (MSTR = SSTR / p and MSE = SSE/(n-p-1), where p=no. of independent variables)
21. How to find f test values from MSTR, MSE? (f = MSTR / MSE)
22. How to find t test values from b1 and S_b1? (t test value = b1 / sb1)
23. When does f = t² (for simple linear or multiple linear regression)?
24. Estimate y for any particular value of x. (Consider the x and y units while estimating the y value).
25. Degrees of freedom in terms of n and p, where n= sample size, and p= number of x variables:
    1. Df numerator (Df₁) = p
    2. Df denominator (Df₂) = n-p-1
    3. Df total (Df_T) =  (n-1)
    4. Sample size = Df total + 1