Study Questions, Lecture 18

Due 11/9

12. Write out the model for simple linear regression for a single observation.

y_i = &beta₁x_i + &beta₀ + &epsilon_i

13. For simple linear regression, write out the formula for the predicted y for a single observation.

y-hat_i = &beta₁-hat * x_i + &beta₀-hat

14. For simple linear regression, write out the formula for the residual for a single observation.

&epsilon-hat_i = y_i - y-hat_i

15. What is another name for the residual?

estimated noise, estimated error, &epsilon-hat

16. Write out the GLM (General Linear Model) versions of:

the statistical model

the parameter estimation equation

the equation for predicted Y, the equation for estimated noise

17. In regression, estimation and tests are only as good as the __________________.

assumed model

18. True or false. The intercept variable must be included in any regression model.

false

19. What is the general matrix formula for the parameter (beta) estimates?

beta-hat = (x'x)^-1(x'y)

20. When we use the Least Squares method for parameter estimation, after setting up the parameter equations, taking the partial derivatives, and setting them equal to zero, the equations we have derived are called the ______________ equations.

normal

21. What do we need to calculate in order to evaluate model adequacy graphically?

The residuals.

22. What can you do if you have replications in a regression study that you can't do without them?

Test the fit of the model

23. What is the common interpretation of R²?

Percent variance accounted for by a model.