IB DP Maths: AI SL复习笔记4.2.3 Linear Regression
Linear Regression
What is linear regression?
- If strong linear correlation exists on a scatter diagram then the data can be modelled by a linear model
- Drawing lines of best fit by eye is not the best method as it can be difficult to judge the best position for the line
- The least squares regression line is the line of best fit that minimises the sum of the squares of the gap between the line and each data value
- This is usually called the regression line of y on x
- It can be calculated by looking at the vertical distances between the line and the data values
How do I use a regression line?
- The equation of the regression line can be used to decide what type of correlation there is if there is no scatter diagram
- If a is positive then the data set has positive correlation
- If a is negative then the data set has negative correlation
- The equation of the regression line can also be used to predict the value of a dependent variable (y) from an independent variable (x)
- The equation should only be used to make predictions for y
- Using a y on x line to predict x is not always reliable
- Making a prediction within the range of the given data is called interpolation
- This is usually reliable
- The stronger the correlation the more reliable the prediction
- Making a prediction outside of the range of the given data is called extrapolation
- This is much less reliable
- The prediction will be more reliable if the number of data values in the original sample set is bigger
- The equation should only be used to make predictions for y
Exam Tip
- Once you calculate the values of a and b store then in your GDC
- This means you can use the full display values rather than the rounded values when using the linear regression equation to predict values
- This avoids rounding errors
Worked Example
c)Another of Barry’s students practises for 15 hours a week, estimate their score. Comment on the validity of this prediction.
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