Chapter 4: Scatter Diagrams and Correlation Flashcards
What is a scatter diagram used for?
To show if there is a relationship between two variables
On which axis is the explanatory variable plotted in a scatter diagram?
x-axis
On which axis is the response variable plotted in a scatter diagram?
y-axis
What symbol is used to plot points in a scatter diagram?
Crosses
True or False: Points in a scatter diagram should be joined up.
False
What defines a positive correlation?
As one variable increases, so does the other
What defines a negative correlation?
As one variable increases, the other decreases
What indicates zero correlation?
The points are randomly scattered
What is linear correlation?
When the points lie close together near a straight line
What is non-linear correlation?
When the points lie close together but the pattern formed is a curve
What is causation?
When one variable causes a change in another
True or False: Correlation implies causation.
False
Give an example of a causal relationship.
Increase in temperature = Increase in ice cream sales
What is an example of correlation only?
Sales of chocolate and sales of clothes having a positive correlation
What does a positive correlation between fat in liver and reaction time imply?
It does not mean one causes the other; there could be a third variable
What is the Line of Best Fit (LOBF)?
A straight line drawn through the middle of the points
What is the significance of the mean point in LOBF?
It has to go through the mean point
What does a closer point to the LOBF indicate?
Stronger correlation
What is interpolation?
Making predictions within the range of given data
What is extrapolation?
Predicting values outside the range of given data
What is the equation of the Line of Best Fit?
y = ax + b
What does ‘a’ represent in the LOBF equation?
The gradient
What does ‘b’ represent in the LOBF equation?
The y-intercept
How is the gradient ‘a’ calculated?
a = (y2 - y1) / (x2 - x1)
What does Spearman’s Rank Correlation Coefficient (SRCC) measure?
The strength of the correlation between two variables
What is the range of values for SRCC?
Between -1 and 1
What indicates a strong positive correlation in SRCC?
r_s near 1
What indicates zero correlation in SRCC?
r_s = 0
What indicates a strong negative correlation in SRCC?
r_s near -1
What is the formula for calculating SRCC?
r_s = 1 - (6 * ∑d^2) / (n(n^2 - 1))
What does Pearson’s Product Moment Correlation Coefficient (PMCC) measure?
The strength of linear correlation between two variables
How does PMCC differ from SRCC?
PMCC tests for linear correlation only
What is a key characteristic of SRCC in comparison to PMCC?
SRCC can be used for non-linear relationships
Fill in the blank: The closer the value of SRCC to 0, the ______ the correlation.
weaker
Fill in the blank: The further the value of SRCC from 0, the ______ the correlation.
stronger
