Question

• Σαπο 54 Σ» = 82 Σα2 = 384 Συ? - 822 Σαμ = 440

Answer 1

Ans : Given that

Σ - 54

y 82

Σ X Ξ 384

12 = 822

Σ χy = 440

sample size = 9

1) Standard deviation of the independent variable X

Σχ2 (Σκ)^2 n η -1 S

(54)^2 384 9 9-1 S =

s_x = 2.7386

2) Standard deviation of the independent variable y

Σy2 - (Σy)^2 n η -1 S

(82)^2 822 9 9-1 S =

Sy=3.0596

3) Covariance

Σχy: η * Χ* y cov(x,y) - η -1

cov(x, y) 440-9*6*9.11 9 - 1

cov(x,y) = -6.4925

4) The Pearson correlation coefficient

γ = η * Σχ*y - (Σκ) * (Σy) [n Σx? - (Σx)^ 2] και [η * Σy? - (Σy)^2]

r = 9* 440-(54) * (82) [9* 384 – 2916] * [9* 822 – 6724]

r_xy = -0.7757

5) To find the line of best fit line

first calculating the   estimating parameter value

$\widehat{\beta_1 } = r_x_y*\frac{s_y}{s_x}$

$\small \widehat{\beta_1 }$ = -0.7757 *(3.0596/2.7386)

$\small \widehat{\beta_1 }$= -0.8666

$\small \widehat{\beta_0 } = \bar{y} -\widehat{\beta_1 }*\tilde{x}$

=9.11 -(-0.8666)*6

=14.3096

The line of the best fit is y = 14.3096 - 0.8666*x