Introduction to regression

118 Further Mathematics
THINK WRITE/DISPLAY
4
5
Find the gradient and y-intercept of the leastsquares
regression line.
Press STAT .
Select CALC and 4:LinReg(ax+b).
After LinReg(ax+b) appears, type L1, L2, Y1.
(To type Y1, press VARS and select Y-VARS
and 1:Function then 1:Y1. Press ENTER .
Write the least-squares regression.
y = −0.63x + 11.73
Press GRAPH to view the data and regression
line. You may need to adjust the WINDOW
settings.
Using arithmetic
Calculate the means.
1
2
Draw up the required table and complete
all calculations.
Column 1: x-values
Column 2: y-values
Column 3: x-deviations from the x mean
Column 4: x-deviations squared
Column 5: y-deviations from the y mean
Column 6: y-deviations squared
Column 7: Product of x- and y-deviations
Total each column.
Note: Sum of columns 3 and 5 is 0.
66
x = -----
8
= 8.25
x y ( )
1 11 –7.25 56.5625 4.5 20.25 –32.625
3 9 –5.25 27.5625 2.5 6.25 –13.235
4 10 –4.25 18.0625 3.5 12.25 –14.875
7 6 –1.25 1.5625 –0.5 0.25 0.625
10 8 1.75 3.0625 1.5 2.25 2.625
12 4 3.75 14.0625 –2.5 6.25 –9.375
14 3 5.75 33.0625 –3.5 12.25 –20.125
15 1 6.75 45.5625 –5.5 30.25 –37.125
66 52 0 195.5 0 90 –124
3 Use the formula to calculate the gradient by Σ( x – x)
( y– y)
substituting values derived from the table.
m =
Σ( x – x)
2
------------------------------------
52
y = -----
8
= 6.5
x – x ( x – x)
2 y– y ( y– y)
2 ( x – x)
( y– y)
4 Use the formula to calculate the y-intercept.
– 124
= ------------
195.5
= −0.6343.
b = y − mx
= 6.5 − (−0.6343)8.25
= 11.733
5 Write the equation of the least-squares linear
regression line.
y = −0.634x + 11.733