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Correlation Coefficient We can see by looking at the graph whether there is a strong or weak correlation between two variables, and whether that correlation is positive or negative. However, there is a mathematical way of working it out, and that is to calculate the correlation coefficient. The correlation coefficient 'r' is a measure of the strength and direction of the linear association between two quantitative variables. This is also known as Pearson's Correlation Coefficient, (Karl Pearson 18571936) represented by the letter r, and it is a single number which ranges from 1 (strong negative correlation) to +1 (strong positive correlation). Correlation coefficients which are close to 1 or +1 indicate a strong correlation. Values close to 0 indicate a weak correlation, with 0 itself indicating no correlation at all. (Java app) Regression by eye A scatter plot is displayed and you can draw in regression lines by hand. You can then compare your lines to the best least squares fit. You can also try to guess the correlation coefficient, r. (link to www.ruf.rice.edu) (or link) another version and another (Java app) Guess the correlation coefficient competition Four scatter plots and 4 correlation coefficients and your task is to match the coefficients to the plots. New plots can be generated and a running score is kept.
Line of best fit If appropriate a line of best fit can be drawn through the points on a scatter plot. Linear Regression is the process for fitting the line (least squares regression) Technology easily fits the line of best fit. Visually judge the fit of the line to the data (Discuss in context) Discuss what the linear model represents and what the gradient indicates (Discuss in context)

Class notes, Class notes McDonalds Example: Scatter plots EXTENSION: More on Correlation coefficient (link to jerrydallal.com) Wikipedia information link to jerrydallal.com with a series of scatterplots with r = 0.7
Quizlet on Scatterplots & Correlation (extension) Calculation and graph of Residuals. Class Exemplar: Class Exemplar: Booklet pg6 
Key Concepts: correlation coefficient 'r' 



Always plot the data and decide VISUALLY, before rushing into linear model and 'r' calculation! 


No linear relationship, but 
Reasonable linear relationship, but there is a better nonlinear relationship! 

Pearson productmoment correlation coefficient 

Which is 'obviously' the same as.... This can be used to calculate 'r' 

eg. The old percentage assessment system
Or it is much easier to use the EXCEL CORREL function
 
Activity: Construct a scatter plot of the data Correl Function Spreadsheet to check out (sigma Ex13.02 #3) Describe the relationship between the variables including the 'r' value 

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Adding a trend line in iNZight 

Make a scatterplot in iNZight (Achieve) Add a linear trend line To add the line of fit: 


Sigma practice 

Ex 13.02 pg 257Ex 13.03 pg 262#1) Data Set

Sigma Ex 13.03
