Chapter 3 lecture

Question 1

difference regression and correlation

Answer 1

a regression line predicts the dependent variable y on the basis of the independent variable x. It describes the relationship between x and the estimated values of y at the various levels of x.

a correlation describes the strength of the association between y and x. It indicates to what extend the data points deviate from the regression line.

Question 2

what happens if r increases

Answer 2

then the data points will be closer to the regression line

Question 3

correlation cannot be used to..

Answer 3

describe the lineair relationship between a and b

Question 4

intercept =

Answer 4

a, value of y when x=0

Question 5

slope =

Answer 5

b, how much y changes if x increases with 1.

Question 6

positive b = … association, negative b = … associaton

Answer 6

positive, negative

Question 7

u should draw the regression line so that…

Answer 7

there are as many dots above as below the line

Question 8

residual

Answer 8

difference between the observation and the prediction (which is the regression line)

Question 9

choose the line with the…

Answer 9

smallest sum of squares

Question 10

sum of squares

Answer 10

sum van (y-y^)^2

Question 11

hoe heet de lijn met de least sum of squares

Answer 11

least squares line

Question 12

if we do not know x, what is the best guess for y

Answer 12

average y!

Question 13

dus wat is het idee achter een regressieanalyse

Answer 13

kijken naar het verschil tussen het average (zonder x) en de regressielijn. how much is the error decreased by adding the predictor?

Question 14

wat is r2

Answer 14

the proportional decrease in the prediction error

Question 15

wat betekenen large/small r2?

Answer 15

large r2 -> groot verschil tussen average and prediction. dit betekent dat je een goede predictielijn hebt!
small r2 -> klein verschil tussen average and prediction. dit betekent dat je een slechte predictielijn hebt, je had net zo goed het gemiddelde kunnen gebruiken! dat geeft dan dezelfde informatie.

Question 16

r2 formule

Answer 16

(total SS - RSS)/total SS

Question 17

wat is SS

Answer 17

SS= total sum of squares = total variance:

vanaf punt tot average/mean (rechte lijn) = 𝒚-

Question 18

wat is RSS

Answer 18

RSS = residual sum of squares

vanaf punt tot regression line = y^

RSS -> R, dus vanaf REGRESSION prediction line

Question 19

wat is de relatie tussen total ss en rss

Answer 19

de RSS zit verwerkt in de total SS

Question 20

total sum of squares (SS) = (formule kort)

Answer 20

SS (y-y-) = RSS (y-y^) + SSR (y^- y-)

Question 21

tekening relatie SS, SSR, RSS

Answer 21

—————- SS (tot mean/average)
———– RSS (tot regressielijn)
——(SSR) (tot regressielijn rest)

Question 22

good regression model =

Answer 22

small RSS
large r2
regression model does better than simply predicting the mean.

Question 23

r2 uitleg definitie

Answer 23

the proportion of variance in y explained by x

Question 24

hoe kan je r ook berekenen

Answer 24

regression coefficient ^2

Question 25

de regressielijn moet de … mogelijke RSS hebben

Answer 25

LAAGST (dan ligt het data punt het dichtste bij de predictielijn)

Question 26

kijken naar samenvatting tekening van rss etc.

Answer 26

oke echt doen he

Question 27

wat als RSS ongeveer = SS

Answer 27

dan r2 = 0

Question 28

wat als SS > RSS

Answer 28

r2 > 0 (goed)

Question 29

wat is de predictor van ss

Answer 29

de mean

Question 30

wat is de predictor van rss

Answer 30

de regressielijn

Question 31

hoe kan je de value van r2 interpreteren

Answer 31

“the variance around the regression line is … % (/100!) less than the total variance.”

Question 32

wat als je de regressie voor de populatie wil testen

Answer 32

𝜇𝑦 =𝛼+𝛽𝑥

Question 33

assumpties van hypothese test regressie

Answer 33

• random
• x and y are linear related
• for every value of x, y is normally distributed with the same standard deviation

Question 34

wat is H0 en Ha bij regressielijn testen

Answer 34

H0: 𝛽= 0 vs HA: 𝛽≠ 0

(of one sided)

Question 35

wat is de mean en sd van de sampling distribution

Answer 35

mean = 𝛽
standard deviation = se

Question 36

hoe p value van slope berekenen

Answer 36

2*t.dist!!

Question 37

hoe bereken je 𝑡.025

Answer 37

t.inv(0,975;df) !!!!!

Question 38

the closer the data points are to the regression line…

Answer 38

the smaller RSS
the larger r2
the smaller SSR

Question 39

explained variance

Answer 39

Explained variance does not
actually mean that we
have explained anything, at least
not in a causal sense. It simply
means that we can use one or
more variables to predict things
more accurately than we could
before. It is the proportion by
which the variance of the
prediction errors shrinks.

Question 40

regression and correlation difference kort

Answer 40

regression indicates what a relationship looks like and how you can predict the variable y.
correlation indicates how strong the relationship is.

Question 41

t becomes (slope and standard error)

Answer 41

larger with larger scope
smaller with larger standard error

Question 42

r2 interpretatie kort

Answer 42

..% of the variance of y can be explained by x

Question 43

wat als regressielijn helemaal verticaal is

Answer 43

r=0

Question 44

residual ander woord

Answer 44

prediction error!

Question 45

relationship between b and r

Answer 45

correlation r is the standardized version of b