Question

Given the following data:
Variable
X
Y
mean:
80
8
Variance:
4
9
coefficient correlation 0.6
what is the most likely value of y when x is 90​

Answer 1

Answer:

y value is 3

Step-by-step explanation:

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Question

If for a bivariate data

x

=10,

y

=12,Var(X)=9,σ

Y

=4 and r=0.6, estimate y when x=5.

Medium

Solution

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Mean of x=10

Mean of y=12

Var(X)=9

Var(Y)=4

2

=16

r=0.6

byx=r.

σ

x

σ

y

0.6×

4

3

=0.45

bxy=r.

σ

y

σ

x

=0.6×

3

4

=0.8

∴(x−10)=0.8(y−12)

x−10=0.8y−9.6

x=0.8y+0.4→1

(y−12)=0.45(x−10)

y−12=0.45x−4.5

y=0.45x+7.5→2

x=0.8y+0.4

y=0.45x+0.75

y=0.45×5+0.75

y=3