5 - Correlation & Regression

Question 1

Are correlation and causation the same thing?

Answer 1

No, just because 2 variables appear correlated doesn’t mean one causes the other

Question 2

How can you tell whether there is positive or negative correlation based on a graph?

Answer 2

• Positive = line of best fit sloping upwards and r value is positive
• Negative = opposite

Question 3

What are the units of correlation?

Answer 3

Unit free

Question 4

What is r? What does it measure?

Answer 4

• Sample correlation coefficient

- Measures both the strength and direction of a linear relationship between 2 continuous variables

Question 5

What is r^2?

Answer 5

• Coefficient of determination

- Whatever this value ends up being, we can say that the 2 variables share __% of their variance in common

Question 6

When would you want to do a 2-tailed test instead of a 1-tailed test?

Answer 6

• 2-tailed test when not sure if it will be positive or negative correlation
• If you suspect either positive or negative then do 1-tailed
• *Be careful though because when doing 2-tailed, the region on each side is alpha/2, so will be a smaller region than 1-tailed which is just alpha (can make you accept the H0 based on 2-tailed when you should deny it with 1-tailed)

Question 7

What is the difference between simple and multiple regression?

Answer 7

• Simple = have 1 predictor looking at 1 outcome
• Multiple = have multiple predictors (more than 1 independent variable) and have multiple ways to see how they collectively predict the dependent outcome measures

Question 8

What is the purpose of regression?

Answer 8

• To see how well one variables predict each other

- If unsure of the prediction, do correlation

Question 9

What do we need to know to describe the regression line?

Answer 9

• The slope (m) – has a clear practical interpretation

- The y-intercept (b) – may or may not have a practical interpretation

Question 10

What is residual value?

Answer 10

• Difference between y observed minus y predicted (y = mx + b)
• *We want to minimize this gap

Question 11

What is the principle of least squares?

Answer 11

Wanting to make the residual value as small as possible by choosing values for b & m that minimize the sum of the squared residual values (SSE)

Question 12

What does it mean when slope is 0?

Answer 12

• No correlation between x and y

- Unlikely to happen even if there is no real relationship between the dependent and independent variables

Question 13

If Ha is that beta doesn’t equal 0, is this 1 or 2 tailed? How do you know?

Answer 13

• When there is an equal sign, it is 2 tailed

- When there is > or < it is 1 tailed

Question 14

What is SST?

Answer 14

• Sum of squares total
• Captures total variation in y
• SST = SSR + SSE

Question 15

What is SSR?

Answer 15

• Sum of squares residuals

- Captures variation in y explained by regression

Question 16

What is SSE?

Answer 16

• Sum of squares errors of prediction

- Captures variation in y not explained by regression

Question 17

How do you calculate r^2 from ANOVA?

Answer 17

r^2 = SSR / SST

Question 18

What are some assumptions for ANOVA?

Answer 18

• x and y must be paired (have to have values for each variable for each patient)
• At least one variable must be independent
• At least one of the variables w/ independent observations must be appropriately normally distributed
• Let y be the variable satisfying the independence and normality assumptions; variability of y shouldn’t change as the other variable changes
• Relationship between the 2 variables must be linear

Question 19

What are some requirements and assumptions for multiple regression?

Answer 19

• Subjects to variables ratio (must have at least 10 subjects for each variable b/c if not, will inflate error – increased chance of type 1 error)
• Normality
• Multicollinearity (when you have several independent variables and some are so close that it messes up the correlation; correlation of 0.7 or stronger between 2 independent variables)

Question 20

How can you fix multicollinearity?

Answer 20

Combine variables or remove a variable