Regression and Correlation

Question 1

Correlation

Answer 1

• degree to which two quantitative variables are related

- does not suggest causation

Question 2

Pearson’s correlation coefficient

Answer 2

• commonly used measure for quantitative parametric data
• correlation ranges from -1 to +1
• no units

Question 3

Regression

Answer 3

-helps predict what the next number is going to be in correlated values

Question 4

Regression co-efficient

Answer 4

• y= a+bx

- b is the regression coefficient and a is the intercept on the y axis

Question 5

Fisher’s transformation

Answer 5

-may be used to compare two correlation coefficients for hypothesis testing

Question 6

Partial correlations

Answer 6

-correlations between two variables after adjusting for a third variable

Question 7

Spearman’s correlation

Answer 7

(rho)

• non-parametric equivalent of pearsons
• used to test the association of variables if at least one is ordinal (ranked)
• assumes ranks are equidistant
• if this is not true then Kendall’s tau will be used

Question 8

How to calculate the value of a and b in the regression calulation

Answer 8

• done using a scatter gram and ‘method of least squares’
• lines drawn from dots on the scattergram back to the line of good fit
• these distances are called residue

Question 9

Multiple linear regression

Answer 9

• several independent variables together predict a single dependent variable
• multivarate technique
• the independent variables are called covariates

Question 10

Collinearity

Answer 10

• when two covariates studied may be highly correlated with each other
• may disturb regression

Question 11

R2

Answer 11

• square of regression coefficient
• also called the coefficient of determination
• used to test goodness of fit or final regression
• it is the proportion of total variation in the dependent variable that can be explained by the independent variable
• measures how well the dependent variable and calculated dependent variable correspond to each other
• ranges from 0 to 1

Question 12

Linear regression

Answer 12

-dependent variable must be continuous

Question 13

Logistic regression

Answer 13

-used if the dependent variable is binary

Question 14

Log-linear analysis

Answer 14

-accommodates only categorical data

Question 15

Bernoulli random variables

Answer 15

-variables that have dichotomous outcomes used in the logistic regression

Question 16

Exponential correlation

Answer 16

• used if one wants to demonstrate the exponential relationship of a variable with a factor such as time
• log transformed values can be plotted against time

Question 17

Polynomial regression

Answer 17

• in some cases of non-linearity, the relationship between dependent variable y and independent variable x could be expressed as Y=Xn, where n may be 2,3,4 etc
• this is polynomial regresion

Question 18

1 in 10 rule

Answer 18

• the number of varibles studied in multiple regression models must not be greater than 10% of sample size
• for logistic regression the number of variable must not be greater than 10% of number of events

Question 19

Stepwise regression

Answer 19

• calculates coefficient of regression and starts with most significant to least significant independent variable and fits them in a stepwise fashion into the regression equation
• some statistically significant variables may not be clinically relevant

Question 20

Forward selection

Answer 20

-confounding variable is treated as covariates

Question 21

Backward elimination

Answer 21

-starts with the full equation and tries to discard covariates one by one according to changes that occur in correlation coefficients

Question 22

Y=a+bX+e

Answer 22

• regression equation
• Y= the dependent variable
• a and b are constants, b is the regression coefficient
• X is the independent variable
• E is the error (random variable with mean of 0 ?!)

Question 23

Key point

Answer 23

-using method of least squares we can find the best linear regression equation with minimum variance of ‘e’