Linear Regression Flashcards
What distribution is the error term described by?
Normal distribution.
What is the ideal sum of squares error?
Very small.
What is the name of the symbols x bar and y bar?
Global means
What is a residual?
A function that describes the error in the fit of the model.
e = y - y(hat)
What are the assumptions of linear regression?
- Error is normally distributed
- No error in the x variable.
- Simple linear model is the true model.
Where is the variance of the error term located graphically?
Width of normally distributed error.
What is SS(T)? What does it tell us?
Total corrected sum of squares. Does the data cover a large range of y? Usually good R value.
What does SS(E) tell us?
How much the data point vary about the regression line.
What is R? What does it tell us?
The coefficient of determination. Tells us how strong is the regression by how much variability is accounted for by the model.
What does a higher standard error of the mean response depict?
That the point is far from the global mean.
What is the 4 types of category when analysing residual plots for model inadequacies?
- Perfectly randomly distributed.
- Unbiased but increasing error - transform, mean of error = 0.
- Unbiased but symmetrical, un-uniform error - transform.
- Not at all uniform - not a linear regressor, global error = 0.
Why is the prediction interval wider than the mean response interval?
Because it depends on the errors of the fitted model and the future observations.
What is the total sum of squares for a two-factor ANOVA?
SS T = SS A + SS B + SS AB + SS E
In a hypothesis test for a two-factor ANOVA, what are the hypotheses being tested?
- No main effect of factor A
- No main effect of factor B
- No interaction AB
What is the rejection criteria for a two-factor ANOVA? What conclusion would rejecting the null hypothesis make?
F0 > F alpha, a-1, ab(n-1)
Rejection would mean there is a significant impact on treatment on response.
