Question

PLEASE PROVIDE STEP BY STEP AS WELL AS FINAL ANSWER

Question 7 (Mandatory) (2 points) 7) Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. x10 3 4 5 12 y 8 2 6 9 12

Answer 1

Solution:

From given data , we prepare a table.

X	Y	XY	X^2	Y^2
0	8	0	0	64
3	2	6	9	4
4	6	24	16	36
5	9	45	25	81
12	12	144	144	144

n	5
sum(XY)	219.00
sum(X)	24.00
sum(Y)	37.00
sum(X^2)	194.00
sum(Y^2)	329.00
Numerator	207.00
Denominator	329.76
r	0.6277
r square	0.3940
Xbar(mean)	4.8000
Ybar(mean)	7.4000
SD(X)	3.9699
SD(Y)	3.3226
b	0.5254
a	4.8782

Now ,

Slope of the regression line is

b = ΠΣxy - (Σκ) Σy) ΠΣχ2 - (Σx)2

  $\therefore$ b = 0.525

Now , y intercept of the line is

a = Σy - bΣΧ n

  $\therefore$ a = 4.878

The equation of the regression line is

$\hat y$ = a + bx

Answer:  $\hat y$ = 4.878 + 0.525x