Question

The table below shows the life expectancy for an individual born in the United States in certain years.

Year of Birth	Life Expectancy
1930	59.7
1940	62.9
1950	70.2
1965	69.7
1973	71.4
1982	74.5
1987	75
1992	75.7
2010	78.7

a) Calculate the least squares line. Put the equation in the form of ŷ = a + bx.

(Round your answers to three decimal places.)

ŷ =_________+_______x

b) Find the estimated life expectancy for an individual born in 1965 and for one born in 1982. (Round your answers to one decimal place.)

Birthdate in 1965:__________ Birthdate in 1982:__________

c) Using the least squares line, find the estimated life expectancy for an individual born in 1860. (Round your answer to one decimal place.) __________________

d) What is the slope of the least-squares (best-fit) line? (Round your answer to three decimal places.) ___________________

Answer 1

	X (Year of Birth)	Y (Life Expectancy)	X * Y	X2	Y2
	1930	59.7	115221	3724900	3564.09
	1940	62.9	122026	3763600	3956.41
	1950	70.2	136890	3802500	4928.04
	1965	69.7	136960.5	3861225	4858.09
	1973	71.4	140872.2	3892729	5097.96
	1982	74.5	147659	3928324	5550.25
	1987	75	149025	3948169	5625
	1992	75.7	150794.4	3968064	5730.49
	2010	78.7	158187	4040100	6193.69
Total	17729	637.8	1257635	34929611	45504.02

Equation of regression line is Ŷ = a + bX
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$
$b = ( 9 * 1257635.1 - 17729 * 637.8 ) / ( 9 * 34929611 - ( 17729 )^{2})$
b = 0.227
a =( Σ Y - ( b * Σ X) ) / n
a =( 637.8 - ( 0.2275 * 17729 ) ) / 9
a = -377.243
Equation of regression line becomes Ŷ = -377.243 + 0.227 X

When X = 1965
Ŷ = -377.243 + 0.227 X
Ŷ = -377.243 + ( 0.227 * 1965 )
Ŷ = 68.8

When X = 1982
Ŷ = -377.243 + 0.227 X
Ŷ = -377.243 + ( 0.227 * 1982 )
Ŷ = 72.7

When X = 1860
Ŷ = -377.243 + 0.227 X
Ŷ = -377.243 + ( 0.227 * 1860 )
Ŷ = 45.0

Slope of the least-squares (best-fit) line

Ŷ = -377.243 + 0.227 X

Slope = 0.227