Simple Regression

Question 1

linear regression

Answer 1

used when the relationship between two variables can be described with a straight line

• proposes a model of the relationship

Question 2

correlation vs regression

Answer 2

• correlation determines strength of relationship between X and y
• regression allows us to estimate how much Y will change as a result of a given change in X

Question 3

terminology in regression

Answer 3

• regression distinguishes between variable being predicted and variable(s) used to predict

Question 4

variable being predicted: y

Answer 4

• outcome variable
• DV (only ever one)
• criterion variable
• verticle axis

Question 5

variable used to predict: x

Answer 5

• predictor variable
• IV(s)
• explanatory variable
• horizontal axis

Question 6

when might we use regression

Answer 6

• to investigate strength of effect x has on y
• estimate how much y will change as a result of a given change in x
• predict future value of y based on x

Question 7

what does regression assume + what does it not tell us

Answer 7

• y is dependent (to some extent) on x
• regression doesn’t tell us if this dependency is causal

Question 8

3 stages of linear regression

Answer 8

1. analysing the relationship between variables: strength and direction (correlation)
2. proposing a model to explain that relationship: model is a line of best fit
3. evaluating the model: assessing goodness of fit

Question 9

regression line

Answer 9

(step 2)
- line of best fit
- intercept: value of y (on line of best fit) when x is 0
- slope: how much y changes as a result of 1 unit increase in x

Question 10

evaluating the model; simplest model vs best model

Answer 10

simplest model:
- using average/mean value of y (predictor) to make estimates
- assumes no relationship between x and y

best model:
- based on relationship between x and y
- regression line

Question 11

sum of squares total

Answer 11

the difference between observed values of y and the mean of y

• variance in y not explained by simplest model
• not required to perform in exam

Question 12

sum of squares residual

Answer 12

the difference between the observed values of y and those predicted by the regression line

• variance in y not explained by regression model
• not required to perform in exam

Question 13

difference between SST and SSR

Answer 13

reflects improvement in prediction using the regression model compared to simplest mode

• goodness-of-fit
• sum of squares of the model
• not required to perform in exam

Question 14

the larger the SSm…

Answer 14

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

Question 15

final thing in goodness-of-fit test

Answer 15

• use ANOVA for F-test to evaluate the improvement due to the model (SSm), relative to the variance the model does not explain (SSr)
• ANOVA uses mean square values instead of SS
• this takes d.f. into account
• provides f-ratio

Question 16

F-ratio

Answer 16

measure of how much the model has improved the prediction of y, relative to the level of inaccuracy of the model

Question 17

interpreting F-ratio

Answer 17

• if regression model is good at predicting y (relative to simplest model) the improvement in prediction of the model (MSm) will be larger, while the level of accuracy of the model (MSr) will be small

e.g. F value further from 0

Question 18

H0 when assessing goodness of fit

Answer 18

regression model and simplest model are equal (in terms of predicting y)

MSm = 0
p < .05 reject H0, regression model is better for the data than simplest model

Question 19

note of SS

Answer 19

you never need to calculate it by hand

Question 20

regression equation

Answer 20

y = bx + a

a-intercept
b-slop

y = predicted value of y

Question 21

linear regression assumptions

Answer 21

• linearity: x and y must be linearly related
• absence of outliers (should be removed)
• normality, linearity and homoscedasticity, independece of residuals
• NO PARAMETRIC EQUIVALENT

Question 22

homoscedasticity of residuals

Answer 22

variance of residuals about the outcome should be the same for all predicted scores

Question 23

SPSS output for regression

Answer 23

in model summary
- don’t need this in write-up

Question 24

ANOVA SPPS output for regression

Answer 24

F = MSm / MSr

if p < .05 it is significant improvement when using regression model vs simplest model

Question 25

SPSS Coefficient table

Answer 25

gives us elements for regression equation

beta: as standard deviation units (others as normal units e.g. £)

Question 26

SPSS coefficient table outputs: t-test

Answer 26

• t-test tests the null hypothesis that value of b is 0
• provides us CIs for slope which we need in write up simple regression)

Question 27

how is r^2 calculated

Answer 27

= SSm/SSt
- (multiple r^2 x100 for a percentage)
- in regression we use this to assume that x explains the variance in y

e.g. distance traveled explains a significant amount of variance in taxi fair, F…P… R^2 = .814 or distance traveled explained 81% of variance in taxi fair

Question 28

square root of r^2

Answer 28

= r
IF WE ONLY HAVE ONE PREDICTOR
(remember we will lose the sign)

Question 29

how do we calculate variance not explained by model

Answer 29

1 - R^2

Question 30

write up

Answer 30

no design
- results in text
- we conducted a linear regression to examine the influence of Y on X. Mean Y (SD, CIs)(from descriptive stats at top of output) and mean X (SD, CIs).
- preliminary analysis confirmed no violation of normality, linearity or homoscedasticity assumptions
- Y explained/ did not explain a significant/not significant amount of variance in X, F(,) = __.__, p < .__, R^2 = __. (ANOVA table for F and p, R in model summary table)
- for every (1 unit e.g. mile) increase in Y (e.e.g journey), X (taxi fair) increased by (slope) (coefficients table), 95% confidence interval limits for slope were [,] (coefficients table)

Question 31

simple regression discussion

Answer 31

the findings suggets that X can be predicted by Y, with longer/shorter/higher/lower Y resulting in higher/lower X