For the Midterm

Question 1

What is the variable Y called?

Answer 1

The response variable

Question 2

What are the X variables called?

Answer 2

The predictor, or explanatory variables.

Question 3

What is multiple linear regression?

Answer 3

It relates one numerical characteristic, the response variable, to one or more predictor or explanatory variables.

Question 4

In multiple linear regression, what do we typically assume about epsilon?

Answer 4

That the epsilon are independent, homoscedastic (same variability) and, if the sample size is small to moderate, that they are approximately normal in distribution.

Question 5

What are regression methods used for?

Answer 5

1) Identify and characterize the relationships between the response and predictor/explanatory variables.
2) Estimate or predict the value of the response variable for combinations of the predictor/explanatory variables.

Question 6

What is the objective of time series analysis?

Answer 6

To identify patterns and trends, and to predict future observations.

Question 7

What does UCLM mean?

Answer 7

Upper confidence limit for regression line

Question 8

What does LCLM mean?

Answer 8

Lower Confidence Limit for Regression Line

Question 9

What does UCL mean?

Answer 9

Upper prediction limit

Question 10

What does LCL mean?

Answer 10

Lower prediction limit

Question 11

What is the simple linear regression model?

Answer 11

Y_i = B_o + B_i*x_i + epsilon

Question 12

How do we denote the ith residual?

Answer 12

e_i

Question 13

How are residuals found?

Answer 13

y_i - y_hat_i

Question 14

What is the prediction interval?

Answer 14

The interval a new value is likely to be in

Question 15

What is the confidence interval?

Answer 15

The interval we’re confident a value we already have is in.

Question 16

What sort of hypothesis test do we run on the slope in multiple linear regression?

Answer 16

We test whether it’s equal to 0 or not! It we reject H_o, then the slope is not 0.

Question 17

What does the analysis of variance do?

Answer 17

Tests to see if there exist two slopes that equal each other, and if they equal zero.

Question 18

What does the SSE tell us?

Answer 18

How much of the model’s variance is due to random error.

Question 19

What does SSE denote?

Answer 19

Sum of Squares due to Error

Question 20

What does SSR denote?

Answer 20

Sum of Squares due to the Model (or our regression)

Question 21

What does the SSR tell us?

Answer 21

How much of our model’s variance is understood by the model.

Question 22

What does R-square tell us?

Answer 22

The proportion of our model’s variance that is understood by the model. (the closer to 1, the more accurate our model)

Question 23

Why do we care about partial regressions?

Answer 23

They help us to see the relationship between Y and a single X!

Question 24

What do we use partial plots to determine?

Answer 24

If there is a linear relationship between Y and each individual X (predictor variable)

Question 25

What is collinearity?

Answer 25

When one or more predictor variables are close to being a linear combination of the other predictor variables.

Question 26

What are symptoms of collinearity?

Answer 26

• The regression coefficients have unlogical “signs” (- or +)
• The regression coefficients are huge in magnitude, and have even larger standard errots
• The individual coefficients are nonsignificant, but when grouped with other coefficients are significant.

Question 27

How can we diagnose collinearity?

Answer 27

1. A correlation matrix (look for variables that seem to have a linear relationship.
2. Regress each predictor variable on all the other predictor variables.
   • Look for high values of R-square
   • A Variance Inflation Factor ≥ 10 suggests collinearity.
3. Look at the condition indices (large values and jumps in the values indicate collinearity.)

Question 28

How can we fix collinearity?

Answer 28

• Backward elimination
• Forward Selection
• “Stepwise”?? Selection

Question 29

How does backward elimination work?

Answer 29

It takes out variables whose p-values are greater than alpha (usually .05)

Question 30

How does forward selection work?

Answer 30

It adds variables that 1) have the highest correlation with the current model, and 2) have a p-value less than alpha.