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IB DP Maths: AA SL复习笔记4.2.2 Correlation & Regression
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月18日 下午2:47
PMCC
What is Pearson’s product-moment correlation coefficient?
Pearson’s product-moment correlation coefficient (PMCC) is a way of giving a numerical value to a
linear relationship
of bivariate data
A
positive value
of
r
describes
positive correlation
A
negative value
of
r
describes
negative correlation
r
= 0 means there is
no linear correlation
r
= 1 means
perfect positive linear
correlation
r
= -1 means
perfect negative linear
correlation
The closer to 1 or -1 the stronger the correlation
How do I calculate Pearson’s product-moment correlation coefficient (PMCC)?
You will be expected to use the statistics mode on your G
DC
to calculate the PMCC
The formula can be useful to deepen your understanding
You
do not need to learn this
as using your GDC will be expected
When does the PMCC suggest there is a linear relationship
?
Critical values
of
r
indicate when the PMCC would suggest there is a linear relationship
In your exam you will be given critical values where appropriate
Critical values will depend on the size of the sample
If the
absolute value
of the
PMCC
is
bigger
than the
critical value
then this suggests a linear model is appropriate
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
It can be calculated by either looking at:
vertical distances
between the line and the data values
This is the
regression line of
y
on
x
horizontal distances
between the line and the data values
This is the
regression line of
x
on
y
How do I find the regression line of
y
on
x
?
How do I find the regression line of
x
on
y
?
How do I use a regression line?
The regression line can be used to decide what type of correlation there is if there is no scatter diagram
If the gradient is
positive
then the data set has
positive correlation
If the gradient is
negative
then the data set has
negative correlation
The regression line can also be used to
predict
the value of a
dependent variable
from an
independent variable
The equation for the
y
on
x
line should only be used to make predictions for
y
Using a
y
on
x
line to predict
x
is not always reliable
The equation for the
x
on
y
line should only be used to make predictions for
x
Using an
x
on
y
line to predict
y
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
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
d) Use the appropriate regression line to predict the score on the maths test of a student who got a score of 63 on the English test.
转载自savemyexams
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