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DPT 513 > Correlation and Regression > Flashcards

Correlation and Regression Flashcards

1
Q

are the IV and DV for correlations and regression continuous, categorical, or both?

A

continuous

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2
Q

what does a correlation describe?

A

the relationship bw 2 variables via a correlation coefficient

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3
Q

t/f: a correlation measures the extent to which 2 variables are associated

A

true

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4
Q

what is the correlation coefficient?

A

describes the relationship bw 2 variables

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5
Q

what is the measure of if scores inc/dec together?

A

correlation

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6
Q

does correlation reflect sameness of scores?

A

no, only the nature of how they change

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7
Q

what are the 2 correlation coefficients?

A

Pearson’s and Spearman’s

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8
Q

what is the parametric correlation coefficient?

A

Pearson’s

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9
Q

what is the nonparametric correlation coefficient?

A

Spearman’s

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10
Q

what is the Pearson’s correlation coefficient?

A

the pattern of change/association of the 2 variables over different values of the variables

describes the strength and direction of the relationship

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11
Q

what letter represents the Pearson’s correlation coefficient?

A

r

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12
Q

what are the assumptions of Pearson’s correlation?

A

Linearity
Independence
Normality (30/more or SW)
Equality of variances

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13
Q

how do we determine normality for Pearson’s correlation?

A

if the n is equal to or greater than 30

if not run the SW test

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14
Q

if you have a Pearson’s correlation coefficient of r=-1, if the correlation perfect pos/neg?

A

perfect neg

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15
Q

if you have a Pearson’s correlation coefficient of r=1, is the correlation perfect pos/neg?

A

perfect pos

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16
Q

what is the range of Pearson’s correlation coefficient?

A

-1 to 1

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17
Q

if you have a pearson’s correlation coefficient of r=0, if this a perfect pos/neg correlation?

A

neither, it has no linear relationship

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18
Q

describe the Pearson’s correlation coefficient of r=.20

A

low positive

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19
Q

describe the Pearson’s correlation coefficient of r=.50

A

moderate positive

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20
Q

describe the Pearson’s correlation coefficient of r=.80

A

high positive

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21
Q

describe the Pearson’s correlation coefficient of r=-.8

A

high negative

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22
Q

what is the interpretation of r=0.9 to 1.0/-0.9 to -1.0?

A

very high correlation

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23
Q

what is the interpretation of r=0.7 to 0.89/-0.7 to -0.89?

A

high correlation

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24
Q

what is the interpretation of r=0.5 to 0.69/-0.5 to -0.69?

A

moderate correlation

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25
Q

what is the interpretation of r=0.26 to 0.49/-0.26 to -0.49?

A

low correlation

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26
Q

what is the interpretation of r=0 to 0.25/0 to -0.25?

A

very low correlation

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27
Q

what are the hypotheses for Pearson’s correlation coefficient?

A

H0: rho=0

Ha: rho is not equal to 0

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28
Q

what does the H0 of rho=0 mean?

A

x and y are not correlated

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29
Q

what does the Ha of rho not equal to 0 mean?

A

x and y are correlated

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30
Q

what is the test statistic of Pearson’s correlation coefficient?

A

r

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31
Q

what are the df of Pearson’s correlation coefficient?

A

n-2

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32
Q

are the hypotheses of Pearson’s correlation coefficient one or two sided?

A

two sided only

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33
Q

how do you report Pearson’s correlation coefficient results?

A

A Pearson correlation was conducted to determine the relationship bw [variables]. There was a statistically significant [strong/moderate/ weak, positive/negative] correlation bw [variable]. (Pearson r=[], p=[]).

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34
Q

what is the conclusion of the following data?

r=0.15
p<0.01

A

the correlation is statistically significant, but has low strength with limited clinical importance

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35
Q

when do we use the nonparametric correlation (Spearman’s)?

A

when the Pearson’s correlation assumptions fail

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36
Q

what are the hypotheses of the Spearman’s correlation coefficient?

A

H0: rho=0 (no correlation)

Ha: rho is not equal to 0

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37
Q

what is the procedure of the Spearman’s correlation coefficient?

A

1) separately rank the x and y data (Rx and Ry)
2) apply the Pearson product moment formula to the ranks

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38
Q

t/f: the interpretation of Spearman’s correlation is the same as Pearson’s

A

true

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39
Q

t/f: the Spearman’s “perfect” correlation looks different than Pearon’s since linearity is not necessary

A

true

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40
Q

how do we report the results of the Spearman’s correlation coefficient?

A

A Spearman correlation was conducted to determine the relationship bw [variables]. There was a statistically significant [strong/moderate/ weak, positive/negative] correlation bw [variable] (Spearman rho=[], p=[]).

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41
Q

what does the Spearman’s correlation evaluate?

A

the relative ording of x and y rather than actual distances from the mean

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42
Q

non linear trends can be better detected by Pearson’s or Spearman’s correlation?

A

Spearman’s correlation

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43
Q

what correlation coefficient is better when the assumptions of Pearson’s fail?

A

Spearman’s correlation

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44
Q

t/f: Spearman’s correlation is slightly worse than Pearson’s when assumptions (LINE) are met

A

true

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45
Q

is there more type 1 or type 2 errors when we use Spearman’s when the assumptions are met?

A

type 1 errors

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46
Q

t/f: correlation is causation

A

FALSE

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47
Q

what is the intraclass correlation coefficient (ICC)?

A

the assessment of the reliability of measurement scales (test-retest, intrarater, interrater, etc)

the association of 2 or more measures and the amount of association

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48
Q

ICC reflects both the _____ __ _____ and ______ bw measurements

A

degree of correlation, agreement

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49
Q

what is the reliability index?

A

the true variance divided by the true variance plus the error variance

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50
Q

what are the ICC assumptions?

A

normality and stable variance

51
Q

if there is a true variance of 9.6 and error variance of 12.8, what is the ICC?

A

9.6/9.6+12.8=0.43

52
Q

what is the range for ICC?

A

0-1

53
Q

t/f: there are no negative values for ICC

A

true

54
Q

what does ICC<0.5 mean?

A

poor reliability

55
Q

what does ICC 0.5-0.75 mean?

A

moderate reliability

56
Q

what does ICC 0.75-0.9 mean?

A

good reliability

57
Q

what does ICC >0.9 mean?

A

excellent reliability

58
Q

when do we use linear regression?

A

when we want to predict DV using IVs

59
Q

what is an example of linear regression testing?

A

researchers want to know how weekly energy expenditure impacts LDL cholesterol levels in ppl who are in their 40s

the blood samples were collected from the antecubital vein bw 8-10am, in a sitting position after 12 hours of fasting and avoiding alcohol and the LDL cholesterol was measured (in mg/dL)

researchers also estimated an index of weekly energy expenditure by examining the type, frequency, duration, and intensity of sports-related physical activity in the past year. The index ranges from 0-50.

60
Q

what is a linear relationship?

A

when 2 variables are related linearly, the relationship can be summarized by a single, straight line

61
Q

simple linear regression is also called what?

A

bivariate regression

62
Q

what is the simple linear regression?

A

the process of identifying a line that best characterizes a linear relationship bw 2 continuous variables

63
Q

what variable is the predictor in regression?

A

IV

64
Q

is the predictor/IV x or y?

A

x

65
Q

what variable is the outcome?

A

DV

66
Q

is the outcome/DV x or y?

A

y

67
Q

when there is 1 IV and 1DV, what is run?

A

simple linear regression

68
Q

every line is characterized by what two things?

A

a slope (a) and an intercept (b)

in the equation y = a(x) + b

69
Q

what is the equation of a line?

A

y = a(x) + b

70
Q

in regression, if x=1, a=4, b=2, what is the y? (bad question, ignore)

A

4

71
Q

linear regression requires what two things?

A

intercept and slope

72
Q

what is the procedure for least squares criterion?

A

1) draw a line through the data

2) calculate the distance of every observation to the line, square it, and add up over all observations

73
Q

t/f: the line with the smallest SS is the best regression line

A

true

74
Q

based on the SS, what is the best regression line?

A

the line with the smallest SS

75
Q

t/f: there is only 1 line the is the best regression line

A

true

76
Q

what is the linear regression equation of point estimation?

A

y = ax + b + epsilon

77
Q

in the equation for point estimation, what does each letter mean?

A

y=value of DV
x=value of IV
a=slope
b=intercept
epsilon=error term

78
Q

when x increases by 1 unit, y increases by ___ units

A

a (slope)

79
Q

what is the linear regression equation?

A

mu of y = ax + b

80
Q

the linear regression equation predicts the mean of _ based on _

A

y, x

81
Q

what is the interpretation of the following: the linear regression equation predicts the mean of y based on x?

A

the mean of y for a given value of x is obtained from the linear equation ax + b

82
Q

is there an error term in the linear regression equation?

A

nope

83
Q

what is the primary research question in evaluating linear regression?

A

are x and y related?

84
Q

the linear regression estimates and tests what?

A

the x-y relationship

85
Q

the linear regression predicts _ using _

A

y, x

86
Q

the x-y relationship is described by what?

A

the slope (a)

87
Q

what are the hypotheses of the simple linear regression?

A

H0: a=0
Ha: a is not equal to 0

88
Q

are the hypotheses for simple linear regression about the slope (a) or the intercept (b)?

A

the slope (a)

89
Q

what are the assumptions of the linear regression?

A

Linearity
Independence
Normality of residuals
Equality

90
Q

is there a nonparametric test for linear regression if the assumption of normality of residuals is violated?

A

nope

91
Q

what is an unspoken assumption of regression?

A

that you have to know which variable is IV and which is DV bc regression requires a clear distinction bw them

92
Q

if it is unclear which variable is the DV or IV, what testing should be done?

A

correlation

93
Q

t/f: it is possible to reject H0 w/a nonlinear trend in regression

A

true

94
Q

what df do we use from the regression F test?

A

regression(1) and residual (n-2)

95
Q

if the p value of the F test are less than or equal to alpha, what does this mean?

A

x and y are linearly related (reject H0)

96
Q

if the p value of the F test is greater than alpha, what does this mean?

A

x and y are not linearly related

97
Q

where do we get the significance level for regression?

A

the ANOVA table significance

98
Q

where do we get the y intercept and slope for the regression equation?

A

from the coefficients table

the constant unstandarized B is the y intercept

the variable unstandardized B is the slope

99
Q

if the variable unstandardized B value is -2.483, what does this mean?

A

for one unit increase in x, there is a 2.48 decrease in y

100
Q

t/f: the inference based on the confidence interval for the slope will match the inference of the F-test

A

true

101
Q

if H0:a=0 is rejected will the confidence interval contain 0?

A

no

102
Q

if H0:a=0 is failed to be rejected, will the CI contain 0?

A

yes

103
Q

if the confidence interval is -7.891 to 0.001, does it contain 0? what does this mean?

A

yes, fail to reject H0

104
Q

if the confidence interval is 0.001 to 7.891, does it contain 0? what does this mean?

A

no, reject H0

105
Q

what is the coefficient of determination, or goodness of fit?

A

r^2

a proportion of the total variation in y that is explained by x in regression

106
Q

what does r^2 tell us?

A

what proportion of the total variation in y that is explained by x in regression

107
Q

if r^2=0 what does this mean?

A

there is no relationship

108
Q

if r^2=1 what does this mean?

A

there is a perfect relationship

109
Q

what does the R coefficient tell us?

A

the strength and direction of the linear relationship

110
Q

if the R is negative, is the slope positive or negative?

A

negative

111
Q

t/f: r^2 tells us the % of y explained by x

A

true

112
Q

if the r^2=.565, what % of the y is explained by x?

A

56%

113
Q

if the data is linear, should we use Pearson or Spearman?

A

Pearson

114
Q

how do we report simple linear regression?

A

Simple linear regression was conducted to investigate the linear relationship between [IV] and [DV].

Results indicated a [significant OR no] linear relationship between [IV] and [DV] (R2 = [], F(regression df, residual df) = [], p = []).

The slope coefficient was [], indicating the [DV] [increased/decreased] by [slope] for each [IV].

The R2 indicated [R2*100]% of the variation in [DV] can be explained by the regression model with [IV].

115
Q

what is the general goal of simple regression?

A

fit a “best” line to 2 continuous variables x and y

116
Q

what are the specific goals of simple regression?

A

test the linear x-y relationship via slope (a)

estimate a and b

use estimated regression equation to predict y bar for values of x

estimate a proportion of total variation in y explained by x in regression

117
Q

what is the difference bw correlation and regression?

A

correlation is a more general method that can be done any time regression can be done, but not vice versa bc regression requires prediction bw IV and DV

regression provides more info w/x-y prediction.

118
Q

t/f: in simple linear regression, the correlation coefficient is a “companion” to the slope and provides related info regarding the slope

A

true

119
Q

what does multiple regression test?

A

more than 1 IV to predict a DV y

120
Q

t/f: the more predictors (IVs) the more accuracy in predicting the y

A

true

121
Q

what is the multiple regression equation?

A

yi=a1x1i+a2x2i+…+apxpi + b + epsilon i

122
Q

what does a1 represent in the multiple regression equation?

A

the regression coefficient for its predictor x1

a slope

123
Q

what is the process of multiple regression testing?

A

1) conduct the F test of the H0: a1=a2=a3…=ak=0
–> 1st determine if any of the coefficients are non-zero (f-test)
–> none of the variables are linearly related

2) p is less than or equal to a in #1- t tests on each individual coefficient (a1=0, a2=0, a3=0, etc)
–> 1 sample t test (comparing to a constant (0))
–> if some coefficients are non-zero, determine which are non-zero

3) p>a in #1-no further testing needed
–> none of the variables are related to DV
–> if all coefficients are zero, no need to test further

DPT 513 (9 decks)

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