Bivariate Data

Question 1

What are properties of bivariate data?

Answer 1

Both variables are considered
Both could be random
Usually displayed on scatter graph
Relationship could be linear (LoBF)

Question 2

What is the PMCC?

Answer 2

Product Moment Correlation Coefficient is used to test to see how strong a correlation is

Question 3

What is the formula for covariance?

Answer 3

S(x_i - xbar)(y_i - ybar) /// n

Question 4

What is covariance?

Answer 4

Covariance gives to what extent points are positively or negatively correlated

Question 5

What is the formula for PMCC?

Answer 5

Covariance /// Standard Deviation

Sum_xy /// Sqr(Sum_xx x Sum_yy)

Question 6

What do the values of PMCC mean?

Answer 6

PMCC = -1 (Perfect Negative Correlation)
PMCC = 0 (No Deviation)
PMCC = 1 (Perfect Positive Correlation)

Question 7

What values of PMCC are considered strong correlation?

Answer 7

r < -0.7
r > 0.7

Question 8

What is the formula for S_xy ?

Answer 8

Sum(x_i y_i) - Sum(x_i)Sum(y_i) / n

Question 9

What is the formula for S_xx ?

Answer 9

Sum(x_i²) - Sum(x_i)² / n

Question 10

How is population correlation coefficient estimated?

Answer 10

Often, a small sample is used to calculate correlation coefficient ‘r’

Question 11

What are the steps to estimating ‘p’ using ‘r’?

Answer 11

Write down the null and alternate hypothesis
Write down significance level
Calculate PMCC(r)
Find critical values from table
Compare ‘r’ to critical value and finding conclusion

Question 12

What is the formula for Spearman’s Rank Correlation Coefficient?

Answer 12

r_s = 1 - Sum(d_i²) /// n(n² - 1)

Question 13

What do the values of SRCC mean?

Answer 13

r_s = 1 is perfect agreement
r_s = -1 is perfect disagreement
r_s = 0 is no agreement or disagreement

Question 14

What does perfect agreement mean?

Answer 14

Ranking is constant in two data sets
Graph is y = x

Question 15

What does perfect disagreement mean?

Answer 15

Where ranking is opposite in two data sets
Graph is y = -x

Question 16

What is association?

Answer 16

Association is any relationship between two variables

Question 17

What is correlation?

Answer 17

Correlation is a subset of association where eh relationship is linear and variables are random

Question 18

Why is SRCC different to PMCC?

Answer 18

In SRCC, association replaces correlation as linear relationship cannot be assumed
r_s = +-1 does not imply perfect agreement/disagreement

Question 19

Why are hypothesis tests used on PMCC?

Answer 19

Hypothesis tests test whether a ‘r’ value is statistically significant as an indicator for ‘p’

Question 20

What is a constant in all hypothesis tests of PMCC?

Answer 20

The null hypothesis suggest that p = 0

Question 21

What is the least squares regression line of y on x?

Answer 21

This is the regressive line for which the sum of the squares of the vertical distance of each point is as small as possible

Question 22

What is the formula for the least squares regression line of y on x?

Answer 22

y = a + bx

Where:
b = Sum(xy) / Sum(xx)
a = ybar - b(xbar)

Question 23

Why might a LOBF not be appropriate in some situations?

Answer 23

If the relationship is non-linear
It may not model some range of values

Question 24

What is the least squares regression line of x on y?

Answer 24

The line for which the sum of squares of the horizontal distance of each point is as small as possible

Question 25

What is the formula for least squares regression line of x on y?

Answer 25

x = a + by _Where:_ b = Sum(xy) / Sum(yy) a = xbar - b(ybar)

Question 26

Why is only one regression line used in real life?

Answer 26

Only one regression line is calculable because one of the variables is controlled (not random) Where ‘x’ is controlled, the line is y on x

Question 27

What is the residual?

Answer 27

The residual of a data point is a measure of the “error” from the regression line

Question 28

What is the formula for the residual for y on x?

Answer 28

r_i = y_i - a - bx_i

Question 29

What is the formula for the residual for x on y?

Answer 29

r_i = x_i - a - by_i

Question 30

What is the residual for y on x?

Answer 30

For y on x, the residual is the vertical distance between point and regression line

Question 31

What is the residual for x on y?

Answer 31

For x on y, the residual is the horizontal line between point and regression line

Question 32

What is the coefficient of determination?

Answer 32

Sum(r_i²) measures how close points are to regression line

Question 33

What does the value of the coefficient of determination mean?

Answer 33

The closer to 0, the worse the model The closer to 1, the better the model

Question 34

What does the coefficient of determination also equal?

Answer 34

Coefficient of determination = PMCC

Question 35

How can a graph show a set of data is appropriate for PMCC?

Answer 35

If the set of points are approximately elliptical on the graph, it suggests bivariate normal distribution, meaning it is appropriate for PMCC

Question 36

What is the conclusion if the 'r' value is greater than the critical value in PMCC and SRCC?

Answer 36

If 'r' > critical value Reject H₀ There is evidence of correlation/association