Karl Pearson's Coefficient of Correlation - Business Mathematics & Statistics Video Lecture | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

so the topic for today is correlation
now remember correlation is a process of
finding out that degree of relationship
between two variables for know what is
that degree of relationship between the
two variables
wherever degree is you know high or
moderate whether the variables are
moderately correlated or highly
correlated this is the objective of
applying this model called correlation
that is the topic for today's class now
correlation can be determined by God
your sons method it can also be
determined by Spearman's
bang
and off for relation and it is also
determined by using method of concurrent
variations so we can determine
correlation by applying any of these
three models fashion denoted by Rd and
method of concurrent negation is denoted
by RC so coefficient of correlation is
determined it can be determined by using
these three models I agree God Pearson's
method here is and coefficient of
correlation for method of concurrent
deviations not where we are going to
apply car Pierce's my heart and by a
time Karl Pearson's method he can return
with the degree of correlation which can
lie between minus 1 to plus 1 so
coefficient of correlation it is always
lying between minus 1 to plus 1 now is
the value of our if it is line which is
0.25 then we can conclude that there is
a low degree of positive correlation
is the value lies between 0.25 two boys
i-5 we can say there is a moderate
degree of positive correlation if the
value of charge is lying between 0.75
plus point 9 9 we can say there is a
high degree of positive correlation and
it is plus 1 that means that is it
perfect positive correlation
so the correlation it will decide you
know that degree of correlation if it is
between 0 to 0.05 that is there is a
degree of positive correlation if it is
get a point two five two point seven
five that means there is a moderate
degree of positive correlation if it is
between plus 0.75 to plus point nine
nine there is an idea of the correlation
and thus one indicates perfect positive
correlation now vice versa if the value
lies between 0 to minus 0.05 then there
is a very good degree of negative
correlation if the value is between
minus 0.25 hundred minus 0.75 there is a
moderate degree or negative correlation
if the value is between minus point
seven five eight minus point nine nine
there India hiding the negative
correlation and the other is minus one
that simplify that is if orphaned
negative correlation that is both are
relievers are no inversely related to
each other that is what the word
Coalition is it means finding out that
degree of relationship between two
variables not only we will be starting
with a cost model that is target
Pearson's method which is denoted by
smaller then we will be proceeding on to
Spearman's method and method of
concurrent aviation and remember there
are no heart till all this
- Tarkenton plus one it cannot go you
know more than plus one and it cannot go
beyond - Panic has to lie between minus
1 to plus 1 now we start with the first
method the our Pearson's method you know
the value of part and also be calculated
by using various models and the first
model take down the formula for
coefficient of correlation by a decline
carbocations method that is direct
method and the formula is summation X
minus X bar into y minus 5 power 4
divided by n summation X minus X bar
whole square by N and salvation by minus
y bar whole square by n so this rate on
this formula which is going to be used
by calculating coefficient of
correlation using carving yourselves
method and the 'days
direct method this formula is direct
method this formula and also he
rewritten as R is equal to PI yawns upon
standard deviation of X bias and
reduction of Y this numerator part
summation X minus X bar into y minus y
bar divided by n it is integrating
and this thumbs while summation X minus
X bar whole square minus 2 in standard
edition of X x square minus mu square is
denoting standard additional fire
so this formula time you hear it as
covariance upon standard edition of
expires compute additional by next some
more advanced X bar which is for as mean
of X is summation X Han and here L
stands for number of observations and by
god it is summation by upon n where
again and stands for number of
observations in my series so our task
before applying this you know bigger
formula the Oh step would be to
completely have a look x bar and y bar
now how we can build in our look expired
I bar now let us denote if we are
finding out the correlation between you
know the march of statistics and
announce so what do we do we are going
to devote this first column by X and we
will denote this second column by Y so
our task will be to fall asleep in both
the first column by X and the second
column i-5 now any of all the others of
X and dividing it by their number the
number if it is equal to 10 so that
value of x bar lady sum of all the
values of x series if I define a
that is then calculate the value of x1
over here it is 250 zion.t / 10 we get
the X is 25 so the first task will be to
calculate lead on your X bar same by our
now how do you get by our add on all the
values of bias CDs total Emma and
divided by the number of observations
they are again equal to 10 so divided by
the number of observations that is 10 we
will get rid out of iOS what we've
already so initially you will have to
calculate the value of x1 and by now see
as the columns are representing X minus
X bar and y minus y bar then X minus X
bar whole Square and Phi minus Phi bar
whole square so we will be you know
constructing the column for X minus X
bar then X minus X bar whole square
after that Phi minus Phi bar and y minus
y bar whole square and ultimately X
minus X bar multiplied
- 500 we are going to calculate it
see how will you calculate 70 - 45 that
will be equal to minus 8 right next 20 -
45 - five four three two - 25 milli -
327 - 25 will be - 25 - 25 a day - 449 -
25 will be equal for what it is - 35
will be 1 then 30 - twenty-five fifty
hundred roof ie 28 - 25 will be equal to
three and forty nine is forty-five will
be equal to five so we will be
calculating the value of X minus X bar
then we'll go for X minus X bar whole
square minus X square will be positive
64 minus five square will be equal to 25
next -3 squared is a nine then 4 minus 4
squared is 16
again 6125
3 squared + 9 + 5 squared will be 25 so
now please add up all these values of
this column X minus X bar whole Square
and anymore
summation of X minus X bar whole square
that is equal to one filtering ID for
now in Beaufort y minus y bar so 22
minus 30 will be my missing 27 is 30
guilty minus 3 next 20-30 will be minus
2 again is 28-30 will be minus 2 29 is
Saturday will be minus 130 minus cuddly
PCO forever - Part A will be when 134 -
30 will be for very high - Part A will
be 5 and 36 minus 30 will give you 6 6
so we will calculate by - I are in
exactly the same fashion as the
calculated X minus X bar now we are
going to find out the value of Phi minus
Phi bar whole square so mu square minus
IR minus beta square will be 64 minus ki
square with equal to 9 minus mu square
will be four again for 1 0 1 square is 1
4 squared 16
5 squared is 25 and 6 squared is 36 how
these add up all the values of this
qualify minus y bar whole square and
this led what is the answer
of summation Y minus y bar mu square is
coming out at 160 so we may have to
calibrate coming of X minus X bar mu
square summation of that next emission
of Y minus R R whole square now in X
target is an important column for X
minus X bar into y minus y bar how over
here we will multiply by a value of X
minus X bar with the corresponding value
of y minus y bar so minus 10 x minus 8
will be 64 minus pi x minus 3 minus
minus will turn positive minus 5 into
minus P will be equal to 15 minus 3 x
minus 26 put into minus 2 will be minus
4 minus 4 into minus 1 will be 4 over
the divers go in the 0 1 into 1 is 1 5
into 4 is 20 3 2 5 is 15 and 5 x 6 with
equal to 30
so now summation of X minus X bar
multiplied by Y minus y bar please tell
me what is the answer
that it's people back we need you 151
now please take out all these values X
minus X 1 X minus X bar mu square Y
minus y bar minus y bar whole Square and
DV DX minus X bar into y minus bi
every day these people get it out now if
there is any problem you can always ask
and if it is true then please see how we
can put all these values in our major
formula to get the value of time
Pearson's coefficient of correlation now
see our summation of X minus s 5i minus
I 1 now summation of X minus X I Y minus
y bar was equal to 151 next number of
observations are equal to 10 over here
now square root of summation X minus X
bar whole square X minus X bar boost
when I was 194 divided by 10 then
summation Y minus I have moves for that
was equal to 160
now see how we are going to save for it
1:50 1/10 on the numerator side you get
a key point 1 then 190 4/10 DP 90.4 and
160 by men that you equal 64 - loop
simply find out the square root of 19
point 4 that is equal to exactly for one
more at least take it up to 3 decimal
places the square root of 19 point four
it is equal to okay four point four zero
four now this will happen if x squared
or 16 that is equal to four
now we will have 4 x 4 point whose your
whole by 4 then what is the value of 4
point 4 0 for x 4 mh17 8 by 6 vs now
solving 15.1 upon 17 points expenses
what is the final answer if you fight
one upon seventeen point six point six
five eight five seven so that is the
value of our Pearson's coefficient of
correlation the value of our it is equal
to 0.85 seventh include raises we can
always give it up at point eight six now
sister is lying between point seven five
two point nine nine so we can always
write our conclusion to get all this
state in our inference part that since
the value is lying between point seven
five point nine nine that is there is a
high degree of positive correlation and
here is your variables that Marx of
these two subjects are highly correlated
II are highly correlated with each other
so this is the significance of
correlation and we did it with the first
model that is tired method keep adding
your son's coefficient of correlation
right