Bivariate Data Analysis, Slides of Mathematics

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Unit 3 – Bivariate Data

Cambridge Ch 1 and 2

2A – Equation of least squares

regression line

• (^) The equation of a linear regression is:

a = y-intercept b = slope

1. You can find the regression

line “by eye”

2A – Equation of least squares

regression line

A.

2A – Equation of least squares

regression line

B. Using your calculator

• You will need to be able to do this in an exam…so practice NOW!!!
• See pg62 for casio fx

2B – How to calculate a residual

• (^) A residual is the vertical distance between the actual data value and

the predicted value.

• (^) The predicted value is the point on the regression line
• (^) Residual = actual value – predicted value
• (^) You will need to be able to:

1. Calculate the value of one residual (example

2B – How to calculate a residual

• (^) You will need to be able to:

1. Calculate the value of one residual (example 3 pg 69)

2. Use Excel to create a residual plot (example 4 pg 70)

1. I will show you how to add “data analysis” toolpack to your Excel

2B – Residual plot 2

B – If there is an identifiable curve in the residual plot then the relationship is non-linear

2B – Coefficient of determination

(R

• How to use coefficient of determination (R 2 ) to assess strength of linear association
• (^) R^2 is the percentage variation in RV that can be explained by EV.
• (^) R^2 = 0.93 means that 93% of the variation in RV is explained by variation in EV
• (^) E.g. 93% of second hand value of car is explained by the age of the car.
• (^) Remember that r is the correlation coefficient (sometimes just called “correlation”)
• (^) Extrapolation – predicting a value inside the range of the data
  • (^) Cannot be sure of the reliability of the prediction
• (^) Interpolation – predicting a value outside the range of data

2B – Performing a regression

analysis 3