Correlation and Regression

Question 1

What is the maximum correlation coefficient that is possible?

Answer 1

1.0
the datapoints are on a perfect line

Question 2

What is the purpose of Correlation?

Answer 2

evaluate the relationship between two variables (x) and (y): f.e. GFR and age

-GFR in the future can be predicted with an equation

Question 3

What can be described by the Correlation line?

Answer 3

-quantitatively describes the
-Strength (described by the correlation coefficient, how close to 1, how close are the data points to the line
-Direction: the positive or negative slope of the line

Question 4

What is the term for the correlation coefficient?

Answer 4

Pearson product-moment coefficient of
correlation (r)

Question 5

Which type of data are used to describe correlations?

Answer 5

-interval or ratio data
in other words: continuous data

Question 6

Which type of data is used for Spearman rho (r2)
Different type of correlation coefficient

Answer 6

Ordinal data
-Ranked

Question 7

General mantra

Answer 7

Correlation does not equal Causation

Question 8

Which conditions are required to establish Causality?

Answer 8

-Controlled conditions
-Randmizedion (RCT), Placebo
-9 Bradford Hill criteria (discussed early in the semester):

biologic credibility of the association, logical time
sequence (cause precedes outcome), a
dose-response relationship, and
consistency of findings across several studies

Question 9

Interpretation of Correlations: R-value

Answer 9

-0.25 indicates little to no relationship
-0.25-0.5 indicates a fair degree of relationship

-0.5-0.75 indicates a moderate to good relationship
-0.75-1.0 is considered good to excellent relationship

Question 10

What is the Coefficient of Determination (r^2)

Answer 10

-indicates the percentage of the total variance in the Y scores, that can be explained by the X scores
-it is explanatory

f.e.: GFR on the y-axis and age on the X-axis -> r=0.9 so the r^2 is 0.81 -> 81% of the Y variable (GFR) can be explained by the changes of the X variable (age)

Question 11

Linear VS Curvilinear

Answer 11

Coefficient r is a measure of linear relationships only

-curvilinear relationships, are not described accurately by the linear correlation coefficient

Question 12

Interpretation of Correlation

Answer 12

-2 variables should not be interpreted solely based on the correlation coefficient r

-variables should be plotted and see whether a linear or curvilinear relationship exists and whether an r value is appropriate

-the assosiation of 0.4 is not twice as strong as 0.2
-the difference in association between 0.5 and 0.6 is not the same as in 0.8 and 0.9

Question 13

Correlation Matrix

Answer 13

-analyzing several variables at one time

-presenting corellation coefficients for all pairs of variables

-each variable will be regressed with each one to see if any of the variables is related to one another

Question 14

Significance of Correlation Coefficient

Answer 14

-the observed correlation is one of an infinite number of possible correlations -> obtained from a random sample of the population
-> subject to sampling error, or BIAS
->need to be tested for statistical SIGNIFICANCE

Question 15

What would be the Null Hypothesis when determining the Correlation Coefficient?

Answer 15

H0 states that r=0 -> no correlation

Question 16

What are the statistical tests used to reject the H0?

Answer 16

-Pearson product-moment coefficient of
correlation

-Spearman rho (r2)

-> to determine the p-value
-if the p-value is less than 0.05, we reject the 0 and state that 2 variables are correlated, DOESN’T mean that there is a STRONG correlation

Question 17

Which factor affects the correlation coefficient?

Answer 17

-Sample Size

-CAUTION:
-with a large sample size statistical significance can be achieved even with a low r-value (0.2, p < 0.05)

Question 18

Can a correlation be extrapolated to values outside the frame it was tested for?

Answer 18

No, it should be limited to the range of values used to produce the correlations

Question 19

Independence of variables

Answer 19

For correlated variables to be considered valid they have to be independent of each other

-dont use related variables -> relatives (mom and children) -> they will give a high correlation value

Question 20

Regression

Answer 20

used to predict the dependent variable (Y) based on the independent variable (X)

-f.e.: (Y) = GFR (X) = Age
-GFR depends on the age

Question 21

What is linear Regression?

Answer 21

-Plotting variables -> creating the line between the data points

-provides an equation that helps to predict the (Y) variable
-Y = m*x +b; (X) = Age

Question 22

What is non-linear Regression used for?

Answer 22

-Curvilinear relationships
-f.e. psychomotor ability and age
-low in kids, peaks at age 30, and declines

Question 23

When to use a Multivariate Analysis

Answer 23

When more than one variable affects variable (Y)
-f.e. Effect of Age and salt intake on GFR

-Often used to develop predictive models of
risk: prediction of cardiac vascular risk based on BP, age, sex, lipids, etc.
-> Incorporate the effect of multiple variables on a single outcome

Question 24

Which type of Regression is used for continuous outcome variables in Multiple Linear Regression?

Answer 24

Multiple Linear Regression

Question 25

What is Logistical Regression used for?

Answer 25

-dichotomous outcomes (variables)

-YES or NO questions
-f.e. to predict the mortality of a patient admitted to the hospital -> Variables (Y): diagnosis, disease state, age, etc -> LIVE or DEATH

-another example: discharge from the hospital at day 3

Question 26

How is Logistical Regression different from Multivariate Analysis?

Answer 26

-Logistical Regression includes multiple variables but the OUTCOME is dichotomous

Question 27

QUESTION

Answer 27

How is the Multivariate Analysis different from the Correlation Matrix?