IB DP Maths: AI SL復習筆記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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