Question

1. In the table below the height, x, in inches and the pulse r minute, for 9 people are given. height (x) Person Pulse rate (y) 68 90 72 85 65 70 100 62 105 75 98 78 70 64 65 68 72 a. Compute the value of the correlation coefficient r and it result. b. Find the equation of the least squares regression line.

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
68	90	1.235	16.901	-4.568
72	85	8.346	0.790	-2.568
65	88	16.901	4.457	-8.679
70	100	0.790	199.123	12.543
62	105	50.57	365.235	-135.90
75	98	34.68	146.679	71.32
78	70	79.01	252.457	-141.23
64	65	26.1235	436.3457	106.7654
68	72	1.235	192.901	15.432

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	622	773	218.889	1614.89	-86.889
mean	69.11	85.89	SSxx	SSyy	SSxy

a)

correlation coefficient ,    r = Sxy/√(Sx.Sy)   =   -0.1461

b)

sample size ,   n    =   9          
here,   x̅   = Σx / n=   69.11                ,         ȳ = Σy/n =   85.89  
                  
SSxx =    Σ(x-x̅)² =    218.8889          
SSxy=   Σ(x-x̅)(y-ȳ) =   -86.9          
                  
estimated slope , ß1 = SSxy/SSxx =   -86.9   /   218.889   =   -0.3970
                  
intercept,   ß0 = y̅-ß1* x̄ =   113.3228          
                  
so, regression line is   Ŷ =   113.3228   +   -0.3970   *x