Week 9 Lecture 9 - regressions

Question 1

When is linear regression used?

Answer 1

when looking at the relationship between two variables
best described with a straight line

Question 2

How does linear regression differ to correlation?

Answer 2

linear regression proposes a model in which you can make estimates from

Question 3

What are x and y in a linear regresion?

Answer 3

y = variable being predicted (outcome variable)
x = variable used to predict (predictor variable)

Question 4

What does a linear regression make the assumption of?

Answer 4

y is dependent on x (to some extent)

Question 5

Does dependency reflect causal dependency?

Answer 5

no just provides evidence for it

Question 6

What are the 3 stages of a linear regression?

Answer 6

1. analyse relationship between variables
2. propose a model to explain relationship
3. evaluate model

Question 7

What does stage 1 of a linear regression involve?

Answer 7

view data in scatterplot, view r value

Question 8

What does stage 2 of a linear regression involve?

Answer 8

the regression line (line of best fit) –> where deviation from data points is smallest

Question 9

What are the properties of a regression line?

Answer 9

a.) the intercept
b.) the gradient (slope)

Question 10

What does stage 3 of a linear regression involve?

Answer 10

assessing goodness-of-fit
how much is the simplest model better than the regression model

Question 11

What does SSt - SSr equal?

Answer 11

SSm

Question 12

the larger SSm the what?

Answer 12

the bigger the improvement in prediction using the regression model over the simplest model

Question 13

What do we use to evaluate SSm relative to SSr?

Answer 13

F-test (ANOVA)

Question 14

What values does an f-test work in?

Answer 14

mean sum values

Question 15

What does the f-ration provide?

Answer 15

a measure of how much the model has improved the prediction of y (outcome) relative to the level of inaccuracy of the model

Question 16

If the regression model is a good fit what will we see?

Answer 16

MSm will be large, MSr will be small
F value will be further from 0

Question 17

What is the null hypothesis in regressions?

Answer 17

regression model and simplest model are equal

Question 18

What are the assumptions for simple linear regression?

Answer 18

• linearity
• absence of outliers
• normality, linearity, homoscedasticity, independence of residuals

Question 19

How do you assess normality, linearity, homoscedasticity, independence of residuals?

Answer 19

consider normal p-p plot –> looking for a straight diagonal

consider residual scatterplot –> looking for a rectangle with clusters towards the centre

Question 20

How can you check whether a data point is an outlier?

Answer 20

check residuals scatterplot
outlier if falls >3.3 or <-3.3

Question 21

Is there a parametric equivalent for linear regressions?

Answer 21

no

Question 22

What is r^2 in regressions?

Answer 22

the amount of variance in y explained by the model relative to the total variance in y
can be expressed as a percentage

Question 23

What is the equation for the regression line in simple linear regression?

Answer 23

y = bx + a

Question 24

What are multiple regressions?

Answer 24

• assess the influence of several predictors on y
• obtain a measure of how much variance in y the predictor variables combined explain
• obtain measures of how much variance in y the predictor variables explain when considered separately

Question 25

What is the regression equation for multiple linear regression?

Answer 25

y = b1x1 + b2x2 + b3x3 … + a

Question 26

What are the 3 stages of a multiple regresson?

Answer 26

1.) analyse relationships
2.) propose a model that is on a plane of best fit
3.) evaluate the model

Question 27

What are the assumptions for multiple regressions?

Answer 27

• sufficient sample size
• linearity
• absence of outliers
• multicollinearity
• normality, linearity, homoscedasticity, independence of residuals

Question 28

What are the formulas for determining sufficient sample size?

Answer 28

if considering combined effects only:
N >= 50 + 8 m

if also considering separate effects:
N >= 104 + m

Question 29

What is multicollinearity?

Answer 29

• x’s correlated with y but not with one another
• check using correlation matrix
• highly correlated x’s (r>.9) can either be combined or eliminated as you are effectively measuring the same thing