Question

If the standard deviation of x and y are 5 and 40/3 and the coefficient of correlation between x and y
is 8/15, then the regression coefficient of y on x is​

Answer 1

Answer:

x=0.625y−0.125

Step-by-step explanation:

x

=3,

y

=5,σ

x

=5,σ

y

=4,r=0.5

b

yx

=r⋅

σ

x

σ

y

=0.5×

5

4

=0.4,

b

xy

=r⋅

σ

y

σ

x

=0.5×

4

5

=0.625

Regression equation,

y−

y

=b

yx

(x−

x

)∣x−

x

=b

xy

(y−

y

)

y−5=(0.4)(x−3)∣x−3=(0.625)(y−5)

y=0.4x+3.8, x=0.625y−0.125

Answer 2

Answer:

The regression coefficient of the y on x measured is​ $\frac{1}{5}$.

Explanation:

Given,

The standard deviation of x, $\sigma_{x}$ = $5$

The standard deviation of y, $\sigma_{y}$ = $\frac{40}{3}$

The coefficient of correlation between x and y = $\frac{8}{15}$

To find,

The value of the regression coefficient of the y on x, $b_{yx}$ =?

As we know,

• The regression coefficient can be calculated by the equation given below:
• $b_{yx} = r\times \frac{\sigma_{x} }{\sigma_{y} }$

Here,

• $b_{yx}$ = The regression coefficient of the y on x
• $\sigma_{x}$ = The standard deviation of x
• $\sigma_{y}$ = The standard deviation of y
• r = The coefficient of correlation between x and y

After putting all the given values in the equation, we get:

• $b_{yx} = \frac{8}{15} \times \frac{5 }{40/3 }$
• $b_{yx} = \frac{8}{15} \times \frac{5 }{40}\times3$
• $b_{yx} = \frac{1}{5}$

Hence, the value of the regression coefficient of the y on x measured =$\frac{1}{5}$.