Week 10 - Correlation and Linear Regression

Question 1

What is the point of a correlation test?

Answer 1

Allows you to examine an association between two scale variables

Question 2

What are the different symbols for the Pearson correlation coefficient and when are they used?

Answer 2

r - when measured from a study sample
rho (𝜌) - when discussing the statistical population

Question 3

What do the values of the Pearson correlation coefficient (r) represent?

Answer 3

Values close to zero means there is no linear association
Values near 1 (positive slope, direct) means x and y increase together and are very close to a straight line (as x increases by one, so does y)
Values between -1 an 0 (negative slope, inverse) mean as y decreases, x increases
Values of 1 or -1 are perfectly correlated positively or negatively

Question 3

What values determine the strength of correlation with the Pearson correlation coefficient?

Answer 3

< 0.3 = weak
0.3 -/< 0.5 = moderate
=/> 0.5 = large

Question 4

What is the notation for the null and alternative hypotheses for correlation tests?

Answer 4

𝐻0: 𝜌 = 0
𝐻𝐴: 𝜌 ≠ 0

Question 5

What is the df notation for correlation tests?

Answer 5

df = n - 2

Question 6

What sampling distribution do t-tests use?

Answer 6

t-distribution

Question 7

What are the assumptions for correlation tests?

Answer 7

Variables X and Y should be scale
Variable X has a linear relationship with variable Y
Both variables should approximate a normal distribution

Question 8

When do you reject the null hypothesis for correlation tests?

Answer 8

p < alpha
𝜌 ≠ 0

Question 9

What is the point of simple linear regression?

Answer 9

To examine whether changes in variable X can predict changes in variable Y when X and Y are numerical

Question 10

Which variables in linear regression are on the x and y axes?

Answer 10

X axis: predictor/exposure/outcome variable
Y axis: outcome/dependent variable

Question 11

What is the equation for simple linear regression?

Answer 11

Y = mx + b + error
Y: outcome
m: slope
x: predictor
b: y-intercept

Question 12

What are the parameters for simple linear regression and what are they used for?

Answer 12

1. intercept
2. slope

Hypothesis testing is done on the parameters of the systematic component

Question 13

What is the notation for the null and alternative hypothesis for linear regression?

Answer 13

𝐻0: 𝛽1 = 0
𝐻𝐴: 𝛽1 ≠ 0

Question 14

What are the assumptions for simple linear regression?

Answer 14

Variable type: outcome must be numeric and predictor can be numeric or categorical
Independence: Y values are independent of one another
Linearity: X and Y have a linear relationship
Normal distribution: Residuals of the relationship are normally distributed (Y has normal distribution around the mean of X)
Homoscedasticity: Y variance is equal for any X value
Consider potential outliers

Question 15

When do you reject the null hypothesis for linear regression?

Answer 15

p < alpha

Question 16

What is the difference between correlation and linear regression?

Answer 16

Correlation: association and correlation
Regression: prediction and causation