W3 Multiple Linear Regression

Question 1

WHAT is multiple linear regression

Answer 1

the linear relationship between the dependent variable y and 2 or more independent x variables

Question 2

equation of line in multiple regression

Answer 2

Y = B0 + B1X1 + B2X2 … + E

Question 3

what is r^2 the coefficient of multiple determination

Answer 3

tells us how much of Y is explained by x independent variables

Question 4

why is using adjusted r^2 more reliable

Answer 4

never decreases degrees of freedom when a new x variable is added to the model

Question 5

what is a residual error

Answer 5

difference between actual and assumption

Question 6

should residuals be random or not

Answer 6

random

Question 7

confidence interval for the population slopeof b

Answer 7

coefficient of B +- t stat*standard error

Question 8

how to know when to reject null hypothesis

Answer 8

f stat > critical f reject

Question 9

how to test contributions of a single variable

Answer 9

test with all variables

test with all variables except the one we’re testting

Question 10

why might you want to test contributions of a single variable

Answer 10

maybe the variable are just getting a leg up from others that already had an effect

Question 11

what does the coefficient of parial determination tell us

Answer 11

how much of the variance is described by 1 variable when the others are held constant

Question 12

when are dummy variables used

Answer 12

when data is categorical

Question 13

what two numbers are used rather than numerical data as the xs in equation including dummy variable

Answer 13

1 for present

0 for absent

Question 14

how to test interaction between independent variables

Answer 14

ssr(all) - ssr(all except new variables) / mse (all)

Question 15

when is logistic regression used

Answer 15

when the Y variable is binary (a dummy variable) eg
prefer A or B
voted or didn’t vote

Question 16

In what industry is logistic regression used

Answer 16

machine learning and AI

Question 17

what is odds ratio

Answer 17

prob of event of interest / 1 - prob of event of interest

Question 18

what is estimated odds ratio

Answer 18

e^ln(odds ratio)

Question 19

what is estimated probabilit

Answer 19

estimated odds ratio / 1 + estimated odds ratio

Question 20

when testing to see if a non liner model should be used, how do we pick the model with the best fit

Answer 20

the one with the highest r^2

Question 21

two types of transformations to transform non linear models into linearones

Answer 21

square root

log

Question 22

what is the problem with collinearity in regression

Answer 22

you cannot hold one variable constant because of the close relationship between variables

Question 23

what to do in the case of colinear variables

Answer 23

avoid regression or choose one to include

Question 24

indications that collinearity has happened

Answer 24

incorrect signs on coefficients
large change in value of previous coefficient when new one is added
variance of model increases when new variable is added

Question 25

how to lower probability of collinearity

Answer 25

remove unimportant variables

Question 26

purpose of a partial f test

Answer 26

to see the level of contribution of variables

Question 27

what is stepwise regression

Answer 27

adding variables 1 by 1

if r^2 goes up, keep the variable, otherwise dont

Question 28

how to create stepwise regression graphs

Answer 28

insert > scatter >

Question 29

how to add trend lines and equations of lines on scatter plots

Answer 29

right click on a point > add trend line and pick the type which gives the best r^2

Question 30

if you have to make a squared or rooted version of a variable, when you select data for regression do you not include the normal version or do you

Answer 30

you do

Question 31

if there is significant interaction between two variables, how can you make them into one variable to simplify the model

Answer 31

multiplying them together and include this new variable in regression analysis, check and see if it improves the model significantly

Question 32

if you had to construct a 95% confidence level interval of slope, where would you find this

Answer 32

in the coefficients table from regression

Question 33

how would you compute and interpret the coefficients of partial determination.

Answer 33

1. perform anova on data with all independent variables
2. perfrom anova on data with variable we are interested in finding the contribution of only
3. find the absolute difference between both of their regression sum of squares
4. get partial f stat by putting ans3^ over MS from first anova
5. get r^2