Advanced Statistics
Advanced statistics involves analysing data using techniques such as regression, correlation, and hypothesis testing to draw meaningful conclusions from bivariate data sets.
What You Need to Know
Key Concept Diagram
Bivariate data shows the relationship between two variables measured on the same subject
Correlation coefficient r measures the strength and direction of a linear relationship
r = 1 means perfect positive correlation; r = -1 means perfect negative correlation
Regression line (line of best fit) is used to predict values from the data
Outliers can significantly affect the value of r and the regression equation
Key Vocabulary
Bivariate data
Data collected on two variables for each subject in a sample
Correlation
A measure of how strongly two variables are related
Regression
A statistical method to model the relationship between variables
Residual
The difference between an observed data point and the predicted regression value
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A correlation coefficient of r = -0.95 indicates:
Question 2
What does a residual represent in regression analysis?
Question 3
If the regression equation is y = 2x + 5, predict y when x = 4.
Key Concepts Summary
- ●Bivariate data shows the relationship between two variables measured on the same subject
- ●Correlation coefficient r measures the strength and direction of a linear relationship
- ●r = 1 means perfect positive correlation; r = -1 means perfect negative correlation
- ●Regression line (line of best fit) is used to predict values from the data
- ●Outliers can significantly affect the value of r and the regression equation