Question

Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:

x	1	2	3	4	5
y	14.4	18.9	14.4	19.6	20.0

Σx = 15; Σy = 87.3; Σx² = 55; Σy² = 1556.09; Σxy = 273.8

(b) Find the equation of the least-squares line. (Round your answers to two decimal places.)

ŷ =

+  x

(c) Find r. Find the coefficient of determination r². (Round your answers to three decimal places.)

r =
r2 =

Answer 1

b)

X	Y	XY	X²	Y²
1	14.4	14.4	1	207.36
2	18.9	37.8	4	357.21
3	14.4	43.2	9	207.36
4	19.6	78.4	16	384.16
5	20	100	25	400

	X	Y	XY	X²	Y²
total sum	15.000	87.300	273.80	55.000	1556
mean	3.0000	17.4600

sample size ,   n =   5          
here, x̅ =Σx/n =   3.0000   ,   ȳ = Σy/n =   17.46  
                  
SSxx =    Σx² - (Σx)²/n =   10.000          
SSxy=   Σxy - (Σx*Σy)/n =   11.900          
SSyy =    Σy²-(Σy)²/n =   31.832          
estimated slope , ß1 = SSxy/SSxx =   11.900   /   10.000   =   1.1900
                  
intercept,   ß0 = y̅-ß1* x̄ =   13.8900          
                  
so, regression line is   Ŷ =   13.89   +   1.19   *x

......................

c)

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.667
      
R² =    (Sxy)²/(Sx.Sy) =    0.445