Exam 1

Question 1

Why use models?

Answer 1

To understand the relationships between variable

To predict future outcomes

To quantify differences between groups or treatments

Question 2

Response variable

Answer 2

the variable that you want to understand/model/predict. aka - y, dependent variable

Question 3

explanatory variables

Answer 3

the variables you know and think that they are maybe related to the response variable that you want to use to figure out a pattern/model/relationship. aka - x, independent variable, predictor variable, covariates

Question 4

model

Answer 4

a function that combines explanatory variables mathematically into estimates of the response variable

Question 5

error

Answer 5

what’s left over; the variability in the response that your model doesn’t capture (error
is somewhat of a misnomer – maybe noise is a better term)

Question 6

Categorical Data

Answer 6

Two outcomes, not numerical

Question 7

Quantitative variables

Answer 7

Numerical

Question 8

Parameter

Answer 8

Describes entire population

Question 9

Statistic

Answer 9

Describes sample

Question 10

The four-step process

Answer 10

1. Choose
2. Fit
3. Assess
4. Use

Question 11

Model Notation

Answer 11

Y = f(X) + e

Question 12

ybar or xbar

Answer 12

averages

Question 13

yhat

Answer 13

estimate

Question 14

Y = ? (Simple Linear Regression)

Answer 14

Beta0 + Beta1*X + e

Question 15

Yhat = ? (Simple Linear Regression)

Answer 15

Beta0 + Beta1*X

Question 16

Naive Model

Answer 16

Mean + Error

Age = Agebar + e

Question 17

Residuals

Answer 17

How far from the prediction line points are

yhat - y

Question 18

Least Squares

Answer 18

Technique to minimize SSE
The value of all squared residuals is at a minimum

Question 19

SSE

Answer 19

SSE =∑(yhat − y)^2

Question 20

Regression Standard Error

Answer 20

σ = sqrt(SSE / n-2)

Question 21

Linearity

Answer 21

If the resuduals resemble a line

Question 22

Independence

Answer 22

Residuals do not depend on time. Don’t get bigger or smaller as plot goes on

Question 23

Normality of Residuals:

Answer 23

The residuals are distributed symmetrically around zero, with no skewness or kurtosis.

Question 24

• Equal Variance of Residuals (homoskedasticity):

Answer 24

Variables have equal variance over time.

Question 25

Standard Error

Answer 25

ei / σhat = yi - yhati/σhat

If greater than 3 it is considered an outliar

Question 26

Leverage

Answer 26

Points that have extreme x values can have a disproportionate influence on the slope of the regression line

Question 27

Hypothesis Testing

Answer 27

H0: B1 = 0
HA: B1 DNE 0

Question 28

Test Statistic

Answer 28

t = B1hat / SE

Question 29

Confidence Interval for Slope

Answer 29

Beta1 +/- t* SE

Question 30

Coefficient of determination

Answer 30

R^2, How much of the variability is explained by the model

Question 31

Partitioning variability

Answer 31

ANOVA
(yi - ybar) = (yhat - ybar) + yi - yhat)

Question 32

SST

Answer 32

∑(yi - ybar)^2

Question 33

SSM

Answer 33

∑(yhat-ybar)^2

Question 34

SST, SSM, SSE Relationship

Answer 34

SST = SSM + SSE

Question 35

R^2 =

Answer 35

SSM/SST

Question 36

Confidence Interval

Answer 36

sqrt(1/n + [x*-xbar]^2/[∑x-xbar^2])

Question 37

Prediction Interval

Answer 37

sqrt(1 + 1/n + [x* -xbar]^2/[∑x-xbar^2])

Question 38

MLR

Answer 38

Y = B0 + B1X1 + B2X2 +…+Bp*Xp + e

Question 39

MLR with categorical data

Answer 39

Parallel slopes model

Question 40

When does p-value explain

Answer 40

p-value < .05