Unit 3

Question 1

What is covariance?

Answer 1

a measure of the relationship between two random variables and to what extent they change together

Question 2

What is correlation?

Answer 2

quantifies the association between two continuous variables (a standardized version of covariance)

Question 3

What is collinearity?

Answer 3

when the independent variables in a regression are correlated, each variable makes little additional contribution

Question 4

what three things does collinearity do?

Answer 4

can inflate the standard error (SE), indicates redundancy in predictors, and associated p-values will be too high and can affect conclusions

Question 5

what is multi-collinearity?

Answer 5

more than two independent variables are highly correlated in a regression

Question 6

what are 6 assumptions that go with correlation?

Answer 6

random sample or representative of population, independent observations, x values are not used to compute y values, x values are not experimentally controlled, both x and y follow a normal (Guassian) distribution, and all covariation is linear, and no outliers

Question 7

when would we use pearson correlation?

Answer 7

with continuous data

Question 8

how does spearman rank correlation coefficient work?

Answer 8

separately ranks X and Y values and then computes the correlation between the two sets of ranks, it looks at the monotonic relationship

Question 9

what is a monotonic relationship?

Answer 9

a function that either increases or decreases consistently across its domain

Question 10

what does the variance inflation factor show?

Answer 10

how combination of independent variables predict each other, 1=no multicolinearity, typically between 2-10

Question 11

what are the 5 steps of principal components analysis?

Answer 11

1. standardize the range of continuous variables
2. compute covariance matrix
3. compute eigen vectors and eigen values of covariance matrix
4. create feature vector to decide what components to keep
5. recast the data

Question 12

what is PCA doing?

Answer 12

transforming a large set of variables into smaller ones that still contains most of the information

Question 13

how does PCA reduce multicollinearity?

Answer 13

seeing how much variable account for by each component is explained by independent variables and uses new components instead of original independents