Maths Apps 12 unit3

Types of data

Categorical - Nominal and ordinal

Numerical - discrete and continuous

Explanatory variable

A variable to predict or explain the changes observed in another variable

Response variable

A variable in which a observable change (response) occurs, hopefully due to the effect of an explanatory variable

Row graph

Should be oriented with the percentage on the horizontal axis

Column graph

Should be written with the percentage on the vertical axis

Direction

Usually has a negative or positive trend/ association

Form

We describe strength as either linear, non-linear or no association

Strength

We describe strength as either strong moderate or weak association

Correlation coefficient

When a relationship follows a linear trend, the strength of the relationship can be described with a correlation coefficient. This is a number between -1 and 1 given the variable r or rxy where x and y are the variables involved. -1 indicates the perfect linear relationship, while 1 suggests the inverse.

Strong positive linear association r

Between 0.75 and 0.99

Moderate positive linear association r

between 0.5 and 0.74

Weak positive linear association r

between 0.25 and 0.49

No linear association r

Between -0.24 and 0.24

Weak negative linear association r

Between -0.25 and -0.49

Moderate negative linear association r

Between -0.5 and -0.74

Strong negative linear association r

Between -0.75 and -0.99

Pearson’s Correlation Coefficient should only be used when:

1. The two variables are numerical

2. The association is linear

3. There are no outliers

Causation

When one variable directly causes change in another variable

Common Response

When another factor (lurking variable) causes both the EV and RV to change

Confounding

When it is unclear how the variables is related and therefore we can’t draw conclusions

Coincidence

When the relationship between the two variables is simply occurring due to a random chance

Line of Best Fit

A straight line that shows the association between variables on a scatterplot and helps us to make predictions

Least squares regression line

Determined by finding the straight line that minimises the sum of the squared difference between the line and each data point.