module 7

Question 1

3 types of associations

Answer 1

• positive: high score predicts high score/low>low
• negative: high score predicts low score/low>high
• no association: scores on first variable dont imply scores on second

Question 2

what does pearsons correlation coefficient assess and what are the cut offs

Answer 2

• most common index of linear regression that assesses magnitude and direction
• range from -1 to 1: 1= perfect positive association, 0= no association, -1= perfect negative association

Question 3

computation of SP

Answer 3

• sum of products of deviation, a index of covariability
• SP= ∑(X-x̄)(Y- ȳ)

Question 4

for sum of products of deviation, what do the following suggest:
- lots of above mean/above mean or below/below values
- lots of below/above or above/below
- equal mix of above and below

Answer 4

• big positive SP value, big negative SP value, Sp value is close to zero

Question 5

r coefficient is covariability of _____ relative to variability of _____

Answer 5

X and Y together, X and Y separately

Question 6

r coefficient formula

Answer 6

r= SP/√SSxSSy

Question 7

as you increase sample size, correlation coefficient will _____

Answer 7

not really change (as both SP and SS increase)

Question 8

r coefficient formula; z score edition

Answer 8

r=∑ZxZy/n

Question 9

z score

Answer 9

• best way of expressing location of a score w in a distribution
• reflects one score’s standing within a distribution of the score

Question 10

coefficient of determination

Answer 10

• correlation squared (r^2)
• proportion of variance in one variable linearly accounted for by the other variable

Question 11

r t test formula

Answer 11

t = r√df/√1-r^2

Question 12

pearsons correlation special cases

Answer 12

• point biserial correlation: dichotomous/cont variable
• phi coefficient: dichotomous/dichotomous variable
• spearman rank order coefficient: ordinal variables

Question 13

factors influencing the size of r

Answer 13

• distribution of variables: perfect is only possible if distribution is exactly pos or neg (same/opposite)
• reliability of measures: perf correlations need perf reliability in both measures
• restriction of range: restriction can attenuate correlations

Question 14

what does (1-r^2) represent

Answer 14

the proportion of variance in the outcome variable that is not explained by the predictor variable

Question 15

simple vs multiple regression

Answer 15

• single: uses single predictor variable
• multiple: uses 2+ predictor variables

Question 16

regression equation

Answer 16

Y=bX+a
y= score of second variable (outcome)
b= slope of best fit line/regression coefficient
X= score of first variable (predictor)
a= y intercept aka regression constant, where x=0

Question 17

total squared error (aka sum of squares error/ SSerror for regression

Answer 17

SSerror=∑(Y-Ŷ)^2
Y= actual score
Ŷ= predicted score
or = (1-r^2)SSy

Question 18

what is used to determine extent to which regression equation fits actual data set

Answer 18

total squared error (SSerror) for regression

Question 19

what equation can be used to find b in linear regression equation

Answer 19

b= SP/SSx
or
= total covariability of X+Y/total variability of X

Question 20

what equation can be used to find a in linear regression equation

Answer 20

a=Ȳ-bX̄

Question 21

when X and Y are z scores, what is the regression equation

Answer 21

Ẑy=rZx
- a=0 sinse X and Y are zero so its dropped

Question 22

standard error of estimate

Answer 22

• measure of standard distance between regression line and actual data points
  =√SSerror/df

Question 23

as r approaches 0, SSerror is ____ but as r approaches 1, SSerror is ____

Answer 23

decreased, increased

Question 24

in simple regression, what is the null hypothesis

Answer 24

• testing if b (slope) value, null=no linear association between X and Y

Question 25

to test null hypothesis of b, you have to split Y into what components

Answer 25

- regression variability: variability in Y predicted from linear association with X - error variability: variability in Y NOT predicted from linear association w/ X

Question 26

f test for regression coefficient

Answer 26

f=variance predicted by regression/error variance or f=MSregression/MSerror

Question 27

SSy= SSregression + ______

Answer 27

SSerror

Question 28

SSregression

Answer 28

=∑Ȳ^2- (∑Ȳ)^2/n or =r^2 SSy

Question 29

SSerror

Answer 29

=∑(Y-Ȳ)^2 or = (1-r^2)SSy

Question 30

degrees of freedom for regression analysis

Answer 30

dfy= df regression - df error dfY=n-1 df error= n-2

Question 31

MS values for regression analysis

Answer 31

MS regression = SSregression/df regression = r^2SSy/1 = r^2SSy MSerror = SSerror/dferror = (1-r^2)SSy/n-2

Question 32

regression assumptions

Answer 32

- independence of observation - linear relationship between X and Y - residuals are normally distributed w a mean of 0 - homoscedasticity of residuals: equal variance around regression line

Question 33

residuals

Answer 33

prediction errors

Question 34

homoscedasticity of residuals indicates ____ for both variability aross line and amount of error

Answer 34

consistancy

Question 35

for regression, where are outliers

Answer 35

they can be on either the DV or IV (predictor or outcome)

Question 36

joint outlier

Answer 36

not an outlier on either DV or IV but an outlier when together

Question 37

alpha in regression

Answer 37

- 2 tailed= .05 norm but if regression has direction/if you have a prediction you can use one tailed

Question 38

beta in regression

Answer 38

similar to t test and anovas (0.2)

Question 39

effect size in regression

Answer 39

- r-index =standardized index of effect size - unstandardized regression coefficient = raw effect size index