Topic 2: Correlation, Simple, and Multiple Linear Regression

Question 1

correlation

Answer 1

displays the form, direction, and strength of a relationship

Question 2

pearson’s correlation

Answer 2

measures the direction & strength of a linear relationship between two quantitative variables

Question 3

covariance

Answer 3

indicates the degree to which x and y vary together

Question 4

interpreting covariance

Answer 4

positive = x and y move in the same direicotn
negative = x and y move in opposite directions
0 = x and y are independent

Question 5

when should we not use r?

Answer 5

• when two variables have a non-linear relationship
• observations aren’t independent
• outliers exist
• homoscedasticity is violated
• the sample size is very small
• both variables are not measured on a continuous scale

Question 6

point-biserial correlation

Answer 6

binary & continuous variables

Question 7

phi coefficient

Answer 7

two binary variables

Question 8

spearman’s rho

Answer 8

• two ordinal variables
• recommended when N > 100

Question 9

kendall’s tau

Answer 9

• two ordinal varibales
• recommended when N < 100

Question 10

counfounder

Answer 10

an association between two variables that might be explained by some observed common factor that influences both

Question 11

lurking factors

Answer 11

potential common causes that we don’t measure

Question 12

partial correlation

Answer 12

the correlation between two variables after the influence of another variable is removed

Question 13

hypotheses for significance of a correlation coefficient

Answer 13

• H₀: ρ = 0 (ρ = population correlation)
  No linear association between the two variables
• H₁: ρ ≠ 0 Linear association between variables

Question 14

simple linear regression

Answer 14

• used to study an asymmetric linear relationship between x and y
• describes how the DV changes as a single IV changes

Question 15

β

Answer 15

the relationship of x on y

Question 16

linear regression equation

Answer 16

• Ŷ = ɑ + βX
• Ŷ = predicted line
• ɑ = intercept
• β = slope

Question 17

method of least squares

Answer 17

• makes the sum of the squares of the vertical distances of the data points from the line as small as possible
• minimizes ss (error)

Question 18

stating hypotheses for the significance of the slope in simple linear regression

Answer 18

• H₀: β = 0 (There is no linear relationship between x & y)
• H₁: β ≠ 0 (There is a linear relationship between x & y)

Question 19

t-test formula

Answer 19

t = sample statistic/ standard error

Question 20

standard error

Answer 20

standard deviation of a sample population

Question 21

assumptions to apply t-test to slope

Answer 21

normal distribution & independence of observation

Question 22

partitioning variance in simple linear regression

Answer 22

• ss (regression) = variation in y explained by the regression line
• ss (error) = variation in y unexplained by the regression line

Question 23

r²

Answer 23

the proportion of total variation in y accounted for by the regression model

Question 24

interpreting r²

Answer 24

0 = no explanation at all
1 = perfect explanation

Question 25

multiple linear regression

Answer 25

explains how the DV changes as multiple IVs change

Question 26

regression plane

Answer 26

Ŷ = ɑ + β₁X₁ + β₂X₂

Question 27

how can we compute a and bⱼ?

Answer 27

using the least squares method

Question 28

standardized regression coefficient

Answer 28

- the effect of a standardized IV on the standardized DV (z-scores) - the change in the standard deviation of the DV that results from a change of one standard deviation in xⱼ

Question 29

stating hypotheses for overall significance in multiple regression

Answer 29

- H₀: β₁ = β₂ = … = βⱼ= 0 (None of the xs are linearly related to y) - H₁: at least one coefficient is not 0 (At least one x is linearly related to y)

Question 30

stating hypotheses for individual regression coefficients in multiple regression

Answer 30

- H₀: β₁ = 0 (Xⱼ is not linearly related to y) - H₁: β₁ ≠ 0 (Xⱼ is linearly related to y)

Question 31

r² in multiple regression

Answer 31

If a new IV is added to the model, SS (Error) will always be smaller and SS (Reg) will always become larger, so r² never decreases when another variable is added to the model

Question 32

adjusted r²

Answer 32

if no substantial increase in r² is obtained by adding a new IV, adjusted r² rends to decrease

Question 33

f-test vs. t-test in linear regression

Answer 33

- simple: f-test = t-test - multiple: can only use f-test