Linear Models

Question 1

What is regression?

Answer 1

A way to study relationships between variables

Question 2

What are the two main reasons we do regression?

Answer 2

• Description and Explanation (genuine interest in the nature of the relationship between variables)
• Preciction (using variables to predict others)

Question 3

Describe the formula for the response

Answer 3

Response = intercept + slope x explanatory variable

Question 4

Describe the intercept

Answer 4

• where the regression line cuts the vertical axis

- the expected value of the response when xi = 0

Question 5

Describe the slope

Answer 5

• the gradient of the regression line

- expected change in the response where xi increases by 1 unit

Question 6

What does the error term allow for?

Answer 6

Deviation from the linear relationship

Question 7

Describe the least squares criterion

Answer 7

Choose values for the parameters to minimise the sum of the squared differences between the observed data and the predicitions under the model

Question 8

What is a residual?

Answer 8

The vertical distances between the observed data and the best fit line

Question 9

What is a best fit line?

Answer 9

A line that minimises the residual sum of squares