Lecture 30- Regression

Question 1

What two variables do we talk about in linear regression?

Answer 1

• Explanatory variable (X), also known as covariate, predictor, or independent variable.
• Outcome variable (Y ), also known as response or dependent variable.

Question 2

How does the nature of the explanatory variable (x) effect how we compare two groups (the x and y)?

Answer 2

• In studies with outcomes on continuous scale we compare means in the two groups
• In studies with binary outcomes, we compare the two groups using odds ratios or relative risks.

Question 3

What are the different types of regression and what are they used for?

Answer 3

Regression in general looks at the relationship between two variables (1 variable= the x explanatory variable, 1 variable= y outcome variable)

Linear regression - used where the outcome is continuous
Logistic regression - used where the outcome is binary

Question 4

What tool allows us to visually see a regression/ relationship?

Answer 4

A scatterplot, explanatory variable is on the x axis and the outcome variable is on the y axis

Question 5

What are the two purposes of simple linear regression?

Answer 5

-To describe the relationship between two variables and test whether
changes in a continuous outcome measure may be linked to changes
in the explanatory variable
-To enable the prediction of the value of the outcome measure given
the value of the explanatory variable.

Question 6

How do we describe a straight line in a pure mathematical sense?

Answer 6

y=mx+c

Question 7

How do we describe a straight line/ linear regression in stats language? What is the ‘extra’ thing we have to account for?

Answer 7

Y = β0 + β1x + e

β0= constant/ y intercept
β1= m/ gradient
e= random error/ the residual term

Question 8

When carrying out statistical modeling what do we assume about the standard error and so what does the linear regression equation become? What is this telling us?

Answer 8

It is assumed that the error terms have zero mean. So the regression model loses the e and becomes…

µY = β0 + β1x.

This is known as the conditional mean µY |x
When you know the true values of β0 and β1 this equation describes how the mean
response changes with x at a population level.

Question 9

Do problems on slide 571

Answer 9

answers on slide

Question 10

What is β1 interpretable as?

What is β0 interpretable as?

Answer 10

• β1 interpretable as change in mean response when x increases by one unit.
• β0 is mean response when x = 0 (as is the y intercept), but may make no sense in many examples.

Question 11

When we are considering e what does it tell us and what do we assume?

Answer 11

-Error term e describes how an individual’s response differs from the mean
of all individuals in population with the same value of x.
-It is usual to assume that the variation in response within any given sub-population (described by x) is normally distributed.
-In other words, we assume that e is a N(0, σ2e) random variable.
-Variance term σ2e describes magnitude of variation in sub-population

Question 12

In a practical sense what is e equal to?

Answer 12

particular value of Y measured - mean

Question 13

Answer the true and false questions on slide 575

Answer 13

Answers on slide