7 Correlation and Regression

Question 1

What is the definition of BIVARIATE DATA?

Answer 1

Data that consists of pairs of values for two random variables.

Question 2

What does correlation measure?

Answer 2

The relationship between two variables.

Question 3

What is Pearson’s Product Moment Correlation Coefficient?

Answer 3

A standardised measure of correlation for linear relationships between two variables.

Question 4

What is the least squares regression line used for?

Answer 4

To make predictions using the equation of the regression line.

Question 5

What is the independent variable?

Answer 5

The variable that is being changed or controlled by the data collector.

Question 6

What is the dependent variable?

Answer 6

The variable that is being recorded.

Question 7

True or False: Correlation implies causation.

Answer 7

False.

Question 8

Fill in the blank: The _______ is the graphical representation of the regression line.

Answer 8

line of best fit

Question 9

What is the purpose of using residuals in scatter graphs?

Answer 9

To identify outliers.

Question 10

What does the term GRADIENT refer to in the context of regression?

Answer 10

The slope of the regression line.

Question 11

What is Spearman’s Rank Correlation Coefficient?

Answer 11

A non-parametric measure of correlation based on the ranks of data.
It is the PMCC of the ranked data.

Question 12

What is INTERPOLATION?

Answer 12

Estimating values within the range of a set of data points.

Question 13

What is EXTRAPOLATION?

Answer 13

Estimating values outside the range of a set of data points or out of the context of the data.

Question 14

What is the PRODUCT MOMENT CORRELATION COEFFICIENT (PMCC)?

Answer 14

A standardised measure of correlation specifically for linear relationships.

Question 15

What does it mean if two variables have CAUSAL CORRELATION?

Answer 15

A change in one variable directly affects the other.

Question 16

Why is a scatter graph important?

Answer 16

To check if the relationship between two variables is linear.

Question 17

What does the term RANK refer to in statistics?

Answer 17

The position of a data point in an ordered list.

Question 18

What is the purpose of calculating the Spearman’s Rank Correlation Coefficient?

Answer 18

To determine the strength of the relationship between the ranks of two variables.

Question 19

True or False: The PMCC is affected by the units of measurement.

Answer 19

False. PMCC is independent of units.

Question 20

What is the purpose of identifying independent and dependent variables in an experiment?

Answer 20

To understand the relationship and effects between variables.

Question 21

Fill in the blank: The _______ is used to describe the strength of correlation.

Answer 21

correlation coefficient

Question 22

Fill in the blank: The Spearman’s rank correlation coefficient is more suitable than the product moment correlation coefficient for _______.

Answer 22

Data which does not follow a bivariate normal distribution

Question 23

What is the equation of the least squares regression line?

Answer 23

y = a + bx, where a is the y-intercept and b is the gradient

Question 24

True or False: A prediction is reliable if it is an extrapolation.

Answer 24

False

Question 25

What does a positive residual indicate?

Answer 25

The actual value is above the predicted value from the regression line.

Question 26

What is interpolation in the context of predictions?

Answer 26

Predicting values within the range of data used to calculate the regression line.

Question 27

What is extrapolation?

Answer 27

Predicting values outside the range of data used to calculate the regression line.

Question 28

How is the value of a interpretted for the line y=a+bx?

Answer 28

When 'x' is 0-'units', 'y' is 'a'-'units'

Question 29

How is the value of b interpretted in the line y=a+bx?

Answer 29

As 'x' increases by 1-'unit', the 'y' increases/decreases by 'b'-'units'

Question 30

What is the definition of a residual?

Answer 30

The difference between the actual value and the predicted value from the regression line.

Question 31

What is the significance of a high PMCC value?

Answer 31

It indicates a strong linear relationship between the variables.

Question 32

What does the graph of the data look like if the SRCC is 1

Answer 32

The data points would form a STAIRCASE

Question 33

What is a TIED RANK?

Answer 33

When ranking the data, if two pieces of data are exactly the same value, this results in a TIED RANK. Allocate each value which needs a tied rank with the mean of the ranks to be allocated.