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PSYC 204 > Chapter 14: Correlation and Regression > Flashcards

Chapter 14: Correlation and Regression Flashcards

1
Q

correlation

A

A statistical method used to measure and describe the relationship between two variables

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2
Q

when do correlations exist

A

when changes in one variable tend to be accompanied by consistent and predictable changes in the other variable

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3
Q

what three aspects of a relationship do correlation measure?

A

the direction, form, and strength

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4
Q

positive correlation

A

two variables change in the same direction

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5
Q

negative correlation

A

two variables change in opposite directions

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6
Q

correlation coefficient

A

Measured by a value ranging from 0.00-1.00, where 0 is no correlation and 1 is a perfect correlation

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7
Q

what types of data use the Pearson correlation?

A

data having linear relationships
data from interval or ratio measurement scales

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8
Q

what type of data uses spearman correlation?

A

used with data from an ordinal scale (ranks)

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9
Q

what type of data uses point biserial correlation?

A

data where one variable is dichotomous and the other consists of regular numerical scores (interval or ratio scale)

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10
Q

when is phi-coefficient used?

A

when you have two dichotomous variables

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11
Q

pearson correlation formula

A

r= covariability of x and y (sp)/ variability of x and y separately (sqrt SSx*SSy)

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12
Q

covariation of x and y

A

sum of (x-mx)(y-my)

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13
Q

pearson correlation z-score formula (sample)

A

r= sum zx zy/ n-1

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14
Q

pearson correlation z-score formula (population)

A

p= sum zx zy/ n

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15
Q

uses of the pearson correlation

A

Used for prediction, validity, reliability, and theory verification

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16
Q

correlation doesn’t equal

A

causation

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17
Q

correlation and restricted range of scores

A

Severely restricted range may provide a very different correlation than would a broaden range of scores
Usually a smaller correlation

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18
Q

outlier

A

deviant individual in the sample

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19
Q

correlations and outliers

A

Outliers provide a disproportionately large impact on the correlation coefficient

20
Q

coefficient of determination

A

Measures the proportion of variability in one variable that can be determined from the relationship with another variable (r²)

21
Q

non-directional Pearson’s correlation hypotheses

A

H0: ρ = 0 and H1: ρ ≠ 0

22
Q

positive correlation hypotheses

A

H0: ρ ≤ 0 and H1: ρ > 0

23
Q

negative correlation hypotheses

A

H0: ρ ≥ 0 and H1: ρ < 0

24
Q

degrees of freedom for correlation hypothesis tests

A

n-2

25
Q

Correlation Hypothesis Test formula

A

t= r-p / sqrt (1-r)2/ n-2

26
Q

How to Test if the Correlation is Different from 0

A

Convert your correlation to a t-value and use the t-table

27
Q

regression

A

a method of finding an equation describing the best-fitting line for a set of data that aren’t perfectly related

28
Q

reasons for regression

A

Make the relationship easier to see
Show the central tendency of the relationship
Predict y-values for given x-values

29
Q

general equation for regression

A

y= bx+ a, where X and Y are variables, a is the intercept and b is the slope

30
Q

best regression line

A

the one that minimizes the prediction error

31
Q

Ŷ

A

the value of y predicted bt the regression line for each value of x

32
Q

(Y-Ŷ)

A

the distance each data point is from the regression line (the error of predictor or residual)

33
Q

Least-squared error solution

A

a line that minimizes the total squared error of prediction

34
Q

how is the regression line calculated?

A

can be calculated with the components of the correlation coefficient

35
Q

slope formula

A

b= SP/ SSx OR b= r sy/sx

36
Q

y-intercept formula

A

a= My- b (Mx)

37
Q

what does a perfect correlation mean?

A

there is no residual/error

38
Q

standard error of estimate

A

how much on average do we expect our predictions to be off?

39
Q

what happens to SEoE as r becomes stronger (0 to 1 or -1)

A

SEoE decreases to 0

40
Q

effect of stronger correlations on the standard error of estimate

A

will result in fewer errors of prediction

41
Q

predicted variability in y scores

A

SSregression = r² SSY

42
Q

unpredicted variability in y scores

A

SSresidual = (1 − r²) SSY

43
Q

Standard Error of Estimate based on r formula

A

SEoE= √(1-r²)SSY/ (n-2)

44
Q

what happens to the regression slope if you standardize scores into z-scores

A

it is equal to the correlation coefficient

45
Q

calculating a regression equation from a correlation

A

Calculate b (slope)
Use b value to calculate a (y-intercept)

PSYC 204 (14 decks)

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