Sharp EL-5103 - Page 25

I ..
statistics.
In Linear Regression there are three Important valu,,; r, e, and b. The correlation
coefficient r shows the relationship bet_en two variables for a partic::ular sample.
The wlue of r is between - 1 and 1. If r equals - 1 or 1, all points on th,
co.-reletion diagram ar e on a line. The further the valu& of r is from - 1 and 1,
the less the points ere massing about ttl, line .nd the 11$$ reliable is ttIe correl.tion .
If r is more th.n 0, it shows. positive corr,lllion IY is in proportion to Xl,nd if
r
;s less t~n O. it is. negatillfl correletion IY il 'nve ... e proportion to Xl .
Th, 'Qullion for the straight line is Y - e + b X. Tha point et which the line crones
the Y exil il •. The slope is b.
Correl.tion coefficient
, .
S,y
[
(1:x)'
I
Js
xx
' Syy
Sxx - 1:x'
----
"
•
a - y-bi
f
Coefficient of linear Syy - Ey'
_ 11:yl'
"
S,y
regression equetion
1:x·1;y
b b ·
Sxy - Exy -
S"
Y-a+b.r
"
x'. y - a
b
y' y'·a.bx
Enimated value !the value of x is estimated from thet of
y.1
Estimated value !the value of y is estimated from that
of .r,)
• Data
for two_rieble statistic:: calculations are inpuned bv the followinll Opllfll'
tlons.
(1) Date (x) ~ Data iy) ~
(21 Data (x) gl] Data (y) 00 FrequencV ~
Eumple: If we know a nudent's mark in mathematic::., can we predict the mark in
Engli sh?
Tha exam marks for six s tu dents chose n al r andom Bfa given in the following table: