Correlation and Linear Regression

Question 1

What type of graph would you use to visualise the relationship between two continuous variable?

Answer 1

Scatterplot

Question 2

What are the two main uses of scatterplots?

Answer 2

▪️Investigate empirical relationship between X (independent) and Y (dependent)
▪️Attempt to predict Y from X

Question 3

What correlation?

Answer 3

How close two variables are to having a linear relationship

‘R’ is used to quantify direction and magnitude

Question 4

What are the two types of correlation coefficient?

Answer 4

▪️Pearson’s
▪️Spearman’s

Question 5

What is the posh was of saying there is a correlation?

Answer 5

There is a linear association

Question 6

What can you determine from the correlation coefficient?

Answer 6

▪️The direction of the effect
▪️The magnitude of the effect

Question 7

When do you use Pearson’s correlation coefficient ‘r’?

Answer 7

To check the magnitude and direction of a linear relationship between two variable

Question 8

What assumptions are needed for Pearson’s correlation coefficient?

Answer 8

▪️Variables are approx. normally distributed
▪️Variables are continuous
▪️Each observation should have a pair of values
▪️No significant outliers
▪️A straight line relationship should be formed (linearity)

Question 9

When should be use Spearman’s Correlation coefficient ‘rs’/’ρ’ ?

Answer 9

When one or both of the variable are NOT normally distributed

Or if the data is ordinal

(less sensitive to extreme influential points)

Question 10

What does Spearman’s Correlation coefficient measure?

Answer 10

▪️Strength and direction of MONOTONIC relationship between two ranked variables
▪️Decrease or increase together but not necessarily at a constant rate as it would if linear

Question 11

What is the non-parametric version of the Pearson’s correlation coefficient?

Answer 11

Spearman’s

Question 12

How Spearman’s Correlation coefficient is calculated depends on whether the data…

Answer 12

▪️Does not have tied ranks
▪️Does have tied ranksn

Question 13

What are the regression coefficients?

Answer 13

β0 (intercept) and β1 (slope)

Question 14

What is the Y variable?

Answer 14

The dependent variable (outcome/response)

Question 15

What is the X variable?

Answer 15

The independent variable (predictor/explanatory/covariate)

Question 16

What is the best linear regression line?

Answer 16

The line closest to all data points (residual ε is as small as possible)

Question 17

How might we estimate the linear regression line?

Answer 17

Ordinary Least Squares (OLS) - minimises the squared residuals to estimate β0 and β1

Question 18

When do we use the Simple Linear Regression Model?

Answer 18

To measure to what extent there is a linear relationship between two variables

Question 19

What is β1 in the null hypothesis?

Answer 19

0

(slope)

Question 20

What assumptions are needed for the simple linear regression model?

Answer 20

▪️There’s a linear relationship
▪️Residuals are independent of one another
▪️Residuals follow normal distribution with mean 0
▪️Homogeneity of variance - size of error doesn’t change significantly across IV

Question 21

What is R?

Answer 21

The simple correlation coefficient

Question 22

What is R squared?

Answer 22

How much the total variation of the DV can be explained by the IV

E.g. 0.270 = 27%

Question 23

How do you interpret a significant p-value in a simple linear regression ANOVA?

Answer 23

The regression model statistically significantly predicts the outcome variable (good fit)

Question 24

What do you use to predict the AVERAGE Y of a specific value of X?

Answer 24

Confidence interval of the MEAN

Question 25

What do you use to predict the specific Y of an individual with a specific value of X?

Answer 25

Confidence interval for the INDIVIDUAL

Question 26

What is the slope coefficient if X is a categorical binary variable?

Answer 26

A measure of the group difference in means (regression line connected mean response of one group to mean response of the other)

Question 27

How do you calculate a regression model with a non binary categorical predictor?

Answer 27

First need to record it into dummy variables

Question 28

A predictor with K levels can be coded as ___ dummy variable but only _______ are necessary to fully represent the predictor.

Answer 28

▪️K ▪️K-1

Question 29

What do you call the dummy variable that is NOT included in the analysis?

Answer 29

The reference category β1 = d1 vs d3 β1 = d2 vs d3

Question 30

How would you interpret a correlation coefficient between 0.6 and 1?

Answer 30

Strong positive (0.8-1 = very strong!)

Question 31

How would you interpret a correlation coefficient between -0.4 and -0.59?

Answer 31

Moderate negative

Question 32

How would you interpret a correlation coefficient between 0.2 and 0.39?

Answer 32

Weak positive

Question 33

How would you interpret a correlation coefficient between 0.0 and 0.19?

Answer 33

Very weak positive/no correlation