Page 27 - Math SL HB Sem 3

Linear Regression

- straight line of best-fit, interpolation and extrapolation.

Regression line:

For a scalter diagram showing at least a moderately strong positive/negative correlation between two
varaibles, a straight line of best-fit (regression line) can be fitted to the graph.

Dependent variable
--rt v

x
xx x
x
xx
lndependent variable
xx
x /

) Equation of regression line:
The equation of regression line of y on r is given by

a-i:pr,-"r

where t is the mean of the x-axis data,
y is the mean of lhe Y-axis data

Llx-x )' o^
sr
-2
.s - iz, is the standard deviation ofx;
n n
(x-i)(v-Y) Lxy LxEy
Sry=X , and is called the covariance
n n nn
ln the examination, you are expected to find this equation using GDC only

GDC

Calculator-T: I C"lculator-C
)Go to 'STAT'and clear all the entries left in the past
'STAT'-'EDIT' -'Ent' u'-'2'- (F6
'l
)Enter the data into list and list 2 correspondingly
'STAT'-CALC'- LinReg(ax+b) L1, L2 I t'CALC'-,REG'- 'X'-'ax+b'
) Read off the value of a and b, lhen write down the equation y ax + b
=

) Graphing the regression line:
O Plot all the data points and the mean point (Br).
@ Draw the line of best-fit (with equation y at + b) through the mean point with the correct
--
slope ('a').

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