Scatter Diagrams And Correlation (4) Flashcards
What is association
Two variables with a relationship between them
What data do scatter diagrams show
Bivariate data
Where do you plot the independent variable
On the horizontal x axis
What does the independent variable show
It shows the value you change
Where do you plot the dependent variable
On the y axis
What does the dependent variable show
The value you do not change
It depends on the explanatory variable
What is correlation
The link between two variables that shows a trend
What is positive correlation
When one variable increases another increases
What is negative correlation
When one increases the other decreases
What is linear correlation
When they lie on a straight line
(This can be positive or negative)
What is non linear correlation
Correlation that shows a curved line
What is a causal relationship
When a change in one variable directly causes a change in another variable.
E.g. The larger a fuel tank the more fuel a car uses
Does correlation directly imply causation
No
Correlation doesn’t always mean there is a causal relationship.
How many factors will cause a change in variables
Multiple.
Although a single scatter graph will show how one factor effects another there may be multiple
What is a line of best fit
A straight line drawn so the plotted points on a scatter diagram are evenly scattered either side of the line
What is a mean point used for
Drawing a more accurate line of best fit (than by eye)
How do you calculate the mean point
The mean x value and mean y value
What is interpolation
Using the line best fit within the given data values to estimate a value
What is extrapolation
Extending the line of best fit further than the given values, to estimate a data value
How reliable is interpolation or extrapolation
Interpolation - reliable as its within the known data values
Extrapolation - unreliable as it is past the known data values
What is the equation for a line / line of best fit
Y = mx + c
In statistics you are likely to see
Y = ax + b
A = gradient
B = y intercept
What is the line of best fit also called
The regression line
What does the line of best fit of a gradient show
The rate of increase of the dependent variable (response variable) to the independent (explanatory) variable
What does the y intercept show
The response variables value when the explanatory variable is 0
What is Spearman’s rank coefficient
r↓s
Shows the strength of correlation
On Spearman’s rank what does each significant value between 1 and 0 show
1 - Perfect positive
0.8 - strong positive
0.4 - weak positive
0 - no correlation
Negative is the opposite
How do you calculate spearman’s rank coefficient
First rank your values using the same scale
Then subtract the two values for your d value
N is the number of groups
Next square this
r↓s = 1- (6× sum of d^2 /n(n^2-1)
What does Pearsons product moment correlation coefficient show
It is similar to spearman’s rank correlation coefficient
It tests for linear correlation.
It tells us how far the data points are from the regression line
It is measured between 1 and -1
