Correlation and Bivariate Linear Regression

Question 1

What is a regression analysis?

Answer 1

The derivation of an equation in which one of the variables (the dependent variable, Y) can be estimated from other variables (the independent variables, X) aka. How movement in the independent variable drives movement in the dependent variable

Question 2

What does the LEAST-SQUARE METHOD do? And what is it also known as?

Answer 2

Draw a ‘line of best fit’ through the data

• The simple ‘regression line’ (linear bivariate regression line)
• A straight line summarising the relationship between X and Y

Question 3

What are the uses of the least squares method?

Answer 3

o Extrapolation – forecast values outside of the range of the sample
o Interpolation – filling in values missing within the range

Question 4

What is correlation?

Answer 4

• Measure of how strong the relationship is between two variables

Question 5

What will correlation sit between? & explain meanings of these

Answer 5

• Will sit between -1 and +1 and is denoted as r
o +1 would be positive and perfect – all observations would fall on the line of best fit
o R=0 is no relationship

Question 6

what would happen to values if they were positively correlated?

Answer 6

• Values that increase / decrease together are positively corelated

Question 7

what would happen to values if they were negatively correlated?

Answer 7

• Values that diverge are negatively correlated

Question 8

What is a Correlation coefficient?

Answer 8

o How well a linear bivariate regression line summarises the data
o A measure of how closely related two variants are