# Stats - Correlation

> Source: https://ollybritton.com/notes/a-level/maths/topics/stats/correlation/ · Updated: 2024-08-25 · Tags: stats, school

## Flashcards
### 2020-12-10
##### What do you call data with two variables??
Bivariate data.

##### What is bivariate data??
Data with two variables.

##### What is correlation??
A measure of the strength and type of a relationship between two variables.

##### ![PHOTO STRONG POSITIVE](paste-108abe33410801007aed82c1ae6c066d12e54352.jpg) What type of correlation is this??
Strong positive correlation.

##### ![PHOTO WEAK POSITIVE](paste-f8594e4d5fd0d8965f02a66482ccedb8e9592e67.jpg) What type of correlation is this??
Weak positive correlation.

##### ![PHOTO STRONG NEGATIVE](paste-10c410e6ab6d91cd3bde5c506d8a180f00c9f790.jpg) What type of correlation is this??
Strong negative correlation.

##### ![PHOTO WEAK NEGATIVE](paste-f8594e4d5fd0d8965f02a66482ccedb8e9592e67.jpg) What type of correlation is this??
Weak negative correlation.

##### ![PHOTO NO CORRELATION](paste-65e11b80963f094fcd60db7f52947164d15a535c.jpg) What type of correlation is this??
No correlation.

##### What's another name for the independent variable??
Explanatory variable.

##### What's another name for the dependent variable??
Response variable.

##### When asked to interpret or describe the correlation between two variables, what must you make sure to do??
State the problem in context.

##### What does it mean for two variables to have a causal relationship??
Changing one variables causes the other to also change.

##### What is the general equation found by a linear regression??
$$
y = a + bx
$$

##### What is a linear regression??
A technique used to come up with a model for a linear relationship.

##### What is the most common type of linear regression??
A Least-Squares Regression.

##### What does a Least-Squares Regression involve??
Finding a line that minimises the distance squared from each point to the line.

##### When can you use a linear regression??
When the correlation suggests there's a linear relationship between two variables.

##### What is interpolating??
Estimating a value inside the range of data.

##### What is extrapolating??
Estimating a value outside the range of data.

##### Which should you use a regression line for: interpolating or extrapolating??
Extrapolating.

### 2022-01-19
##### What does $r$ normally represent in stats??
The PMCC (product moment correlation coefficient) for a sample.

##### What does $\rho$ normally represent in stats??
The PMCC for an entire population.

##### What is the range of the product moment correlation coefficient (PMCC)??
Between -1 and 1.

##### What do values of a PMCC $r$ greater than $0.7$ or less than $-0.7$ correspond to??
A strong correlation.

##### What does a PMCC $r$ value of $0$ correspond to??
Zero correlation.

##### How can you work out the line of best fit and correlation coefficient for two variables??
Using the $y = a + bx$ option on the calculator.

##### What are you using a PMCC for when doing a hypothesis test??
Seeing how likely it is that a sample is correlated given the population size.

##### What is typically the null hypothesis $H_0$ for using a PMCC??
$$
H_0: \rho = 0
$$

##### When doing a hypothesis test for a PMCC/correlation coefficient, what letter do you normally use and why??
$\rho$ because you're thinking about the whole population.

##### Where can you find the critical values for a PMCC/correlation coefficient hypothesis test??
In the formula booklet.

##### What does an alternative hypothesis look like for a PMCC/correlation coefficient where you're testing if there's any correlation??
$$
H_1: \rho \ne 0
$$

##### What does an alternative hypothesis look like for a PMCC/correlation coefficient where you're testing if there's negative correlation??
$$
H_1: \rho < 0
$$

---
Olly Britton — https://ollybritton.com. Machine-readable index: https://ollybritton.com/llms.txt