Question

Use the given data to find the equation of the regression line. Round the final values to tenths, if necessary. Points: 5 17) 1.2 1.4 1.6 1.8 2.0 54 53 55 54 56 How did you find the equation of the regression line?

Answer 1

Solution :

X	Y	XY	X^2	Y^2
1.2	54	64.8	1.44	2916
1.4	53	74.2	1.96	2809
1.6	55	88	2.56	3025
1.8	54	97.2	3.24	2916
2	56	112	4	3136

b = ΠΣxy - (Σx)(ΣΥ) ΠΣχ2 - (Σx)2
  
a = Σy - bΣΧ n

n	5
sum(XY)	436.20
sum(X)	8.00
sum(Y)	272.00
sum(X^2)	13.20
sum(Y^2)	14802.00
Numerator	5.00
Denominator	7.21
r	0.6934
r square	0.4808
Xbar(mean)	1.6000
Ybar(mean)	54.4000
SD(X)	0.2828
SD(Y)	1.0198
b	2.5000
a	50.4000

The equation of regression line,

$\hat y$ = a + bx

$\hat y$ = 50.4 + 2.5x