MR and Dummy
What is the alternative hypothesis for a MR t-test for additional predictor X2?
Ha: B2 =/ 0, accounting for B1 in the model
When can we NOT use R2 and WHY
With Multiple Regression, because R2 always gets bigger when you add more x variables -> so it is not an accurate depiction of how good the model is
Where are CI and PI the narrowest?
When x is close to the mean
What are the assumptions that we check with Simple Linear Regression?
Linearity, Independence, approximate Normality, Equal Variance
What can you ALWAYS check to see if your model has improved?
Se and R2 (or R2 adj)
What is the difference between an F test and a t test?
F tests are for multiple variables, t tests are for just one variable
What happens to r when you convert x from feet to inches?
Nothing, r is unitless
Which is wider (CI or PI) and why?
-single values vary more than means AND there is an extra +1 in the PI equation (so it will always be bigger)
What is a high leverage point?
a point FAR from the mean of x
What is the population model for SLR?
Y = B0+B1X+E
You have X1 = crowd size, X2 = temperature, and X3 = beach, with categories Avila, Pismo, Grover, and Shell -> how many total variables will you have? How many will be dummy variables?
5 total variables, 3 of which being dummy variables
How can you compute Se?
sq root MSE!!!!
What are the SE for CI and PI?
for CI -> SE(fit) and for PI -> SE(prediction)
What would show a violation of the Equal Variation assumption?
A fan shape (or another pattern) in the residual plot
If our CI for the slope is (2,4) what do we decide about the relationship between X and Y/what would the conclusion to this test be?
We would reject the null hypothesis because 0 is not within the interval. There is evidence of a relationship between X and Y
Model 1: X1 X2 X6 and Model 2: X1 X2 X3 X4 X5 -> are these nested? Why or why not?
Not nested because we don't have a true reduced and full model; all of the variables in one are not in the other
What happens to r if you swap the roles of x and y?
r stays the same
We are estimating the mean height (in inches) for all people who weigh 150 pounds and get an interval of (60,70) -> interpret at a 95% confidence level
We are 95% confident that the true mean height for all people who weigh 150 pounds is between 60 and 70 inches
If a point follows the trend but has an extreme x value, what kind of unusual point is this?
High leverage point, but not influential (because in line with the trend)
If I increase n, what happens to the width of a confidence interval? WHY?
It gets narrower because the bigger your sample, the more precise your prediction can be
if yhat(pismo) = 30 +10(temp) +15(avila) +12(avila*temp) -> what is our baseline, and what would our simplified equation look like?
baseline is pismo; yhat(pismo) = 30+10(temp)
Interpret an R2 of 0.88
88% of the variability in Y is explained by X
When could a CI and a PI be the same size?
Only if Se = 0 (which would mean a perfect linear relationship)
What plots can you look at to check the Linearity Assumption? And why should you check BOTH?
Check the X vs Predicted Y scatterplot AND the Residual vs Predicted Y scatterplot -> because a nonlinear pattern might only be visible in the Residual plot
We perform a MUT test, then a MR t-test, then we add a dummy variable, then we add an interaction variable. How many different outputs/equations would we need to look at to find the test statistics for each test?
3 separate outputs