Lecture 8

Question 1

2 Types of Correlation:

Answer 1

Linear and Curvilinear

Question 2

What is Correlation?

Answer 2

When there is a strong relationship between two variables

Question 3

How is strength of correlation measured?

Answer 3

A correlation coefficient. “Ρ” (rho) is used to describe population data correlation. “r” is used when describing sample data

Question 4

Most common measure of correlation

Answer 4

Pearson Correlation Coefficient

Question 5

Limitations of Correlation

Answer 5

Cannot make statements about cause and effect from correlation alone. Correlation and significance are not the same thing. Correlation tells us about linear relationships between variables – BUT many variables can be strongly related but the nature of this relationship is nonlinear (E.g. effort to go from 0% - 20% on an exam is not the same as the effort to go from 60% to 80%)

Question 6

Type of modelling used to display data

Answer 6

Empirical modelling

Question 7

Explanatory variables

Answer 7

Determined by the experimenter. Could be known as: Independent variable, regressor, predictor. Found on horizontal axis.

Question 8

Response variables

Answer 8

Changes as a result of changes to the explanatory variable. AKA: Outcome variable, dependent variable, measured variable. Found on vertical axis

Question 9

Regression Equation:

Answer 9

Y = 𝜶̂ + 𝜷X ̂

In the Least Squares model, we want to chose values for α and β that minimise the sum of the squared errors

Question 10

What are residuals?

Answer 10

Represent the difference between the observed values and the predicted values

Question 11

Regression Analysis Limit

Answer 11

Upper and lower limits may exist, model usually only useful for predictions within the measured range. Take care when extrapolating!

Question 12

Regression Analysis

Answer 12

A method to assess and quantify the relationship between one variable (the dependent variable) and one (or more) independent variables

Question 13

Linear Regression

Answer 13

Used when there is a linear relationship between the variables (dependent and independent). Typically used to calculate an R-Squared (goodness-of-fit) measure

Question 14

R-Squared Measure

Answer 14

Tells us the proportion of variability in the response that is accounted for by the model.

R-squared =1: line perfectly explains data (never happens)

R-squared = 0: model explains no variation