Question

3-The table below lists ages of driver and the cost of their insurance per year 17 18 20 19 21 21 20 18 20 Driver ages 2500 2350 2100 2300 1800 2100 2150 2500 1980 Insurance cost Use a-.10 to test claims If there is a correlation b) what would be the age of a driver if the cost of Insurance is $2750?

Answer 1

X :- Insurance cost

Y :- Driver age

ΣX = 19780
ΣY = 174
ΣX * Y = 380000
ΣX2 = 43915400
ΣY2 = 3380

((N + ΣΧΥ) - ΣΧΣΥ)/((ΝΣ(Χ2) - (ΣΧ)2] (ΝΣ(Y2) – (ΣΥ)2)

$r = ( ( 9 * 380000 ) - 19780 * 174 ) / ( \sqrt{ ( 9 * 43915400 ) - ( 19780 )^{2} )( 9 * 3380 ) - ( 174 )^{2} })$
r = -0.906

To Test :-
H0 :- ρ = 0
H1 :- ρ ≠ 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( -0.9061 * √(9 - 2) ) / (√(1 - 0.821) )
t = -5.66629

Test Criteria :-
Reject null hypothesis if t < -t(α,n-2)
t(α/2,n-2) = t(0.1/2 , 9 - 2 ) = 1.895
t < -t(α/2, n-2) = -5.66629 < -1.895
Result :- Reject null hypothesis

Conclusion :- There is statistical correlation between variables

Part b)

Equation of regression line is Ŷ = a + bX
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = -0.005
a =( Σ Y - ( b * Σ X) ) / n
a =( 174 - ( -0.0054 * 19780 ) ) / 9
a = 31.297
Equation of regression line becomes Ŷ = 31.297 - 0.005 X

When X = 2750
Ŷ = 31.297 + -0.005 X
Ŷ = 31.297 + ( -0.005 * 2750 )
Ŷ = 17.55