Question

Question 1 5 pts η Σαν Σ:Σν Given for formula for the correlation coefficient " = the formulations V- 22-(02) 92-()2 of the slope and intercept in the estimated simple linear regression model y = mx + b where η Σαν-Σε Σν and b= y - ma; using the table below, m= NOTE: Sums given in blue What is the correlation coefficient? 2 ny 1 5 y 15 21 13 9 y? 225 441 169 81 15 105 104 135 64 8 15 16 21 25 91 4 1 25 64 225 256 441 625 1637 16 1 2 65 21 50 1 4 937 494

Answer 1

Answer:

Formula for the correlation coefficient, r, is given as -

Υ Y = ηΣτg - ΣτΣ! VnΣτ2 – (Σ)? γηΣυ? – (Συ)2

Also, the formula of the slope and intercept in the estimated simple linear regression model  
y = mx + b

where   
fir Tu m ΣΑΣ! ηΣτ2 – (Στ)2
and   $b = \bar{y}-m\bar{x}$

Given data :

	T		fic	T	$y^{2}$
	1	15	15	1	225
	5	21	105	25	441
	8	13	104	64	169
	15	9	135	225	81
	16	4	64	256	16
	21	1	21	441	1
	25	2	50	625	4
Total	T6 = 1 Σ	$\sum y = 65$	$\sum xy = 494$	$\sum x^{2} = 1637$	y2 = 937

Using the above information, we can find the correlation coefficient for the given data as -

Υ Y = ηΣτg - ΣτΣ! VnΣτ2 – (Σ)? γηΣυ? – (Συ)2

  $= \frac {7 (494)- (91)(65)} { \sqrt{ 7(1637) - (91)^{2} } \sqrt{ 7(937) - (65)^{2} } }$

  $= \frac {3458- 5915} { \sqrt{ 11459 - 8281 } \sqrt{ 6559 - 4225} }$

  $= \frac {-2457} { \sqrt{3178 } \sqrt{2334} }$

   (rounded to 4 decimal places)

Thus, the correlation coefficient for the given data is approximately -0.9021 .