Question

Q6- Listed below are the body lengths (in inches) and weights (in lb) of randomly selected bears:

Length	40         64         65         49         47
Weight	65        356       316        94         86

a. Find the value of the linear correlation coefficient.

b. Letting y represent weights of bears and letting x represent their lengths, find the regression equation.

c. Based on the given sample data, what is the best predicted weight of a bear with a length of 72.0 inch?

Please write the answer in details.

Answer 1

Ans:

	Length,x	weight,y	xy	x^2	y^2
1	40	65	2600	1600	4225
2	64	356	22784	4096	126736
3	65	316	20540	4225	99856
4	49	94	4606	2401	8836
5	47	86	4042	2209	7396
Total	265	917	54572	14531	247049

a) linear correlation coefficient,r=(5*54572-265*917)/SQRT((5*14531-265^2)*(5*247049-917^2))=0.964

b)

slope,b=(5*54572-265*917)/(5*14531-265^2)=12.286

y-intercept,a=(917-12.286*265)/5=-467.76

y'=12.286x-467.76

predicted weight=12.286*length-467.76

c)

when x=72

predicted weight=12.286*72-467.76=416.83