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Obtain the equation of the line of regression of cost on age from the following table giving the age of a car of certain make and the annual maintenance cost.

Also find the maintenance cost if age of the car is 9 enter image description here

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Let $a = 5, b = 8, c = 1$

Here $n = 4$

enter image description here

$$\overline x=a+c\overline u=a+c.\dfrac {\sum u}n=5+1\times \dfrac 04=5$$

$\overline y=b+c\overline v=b+c.\dfrac {\sum v}n= 8+1\times \dfrac {0.5}4\\ byx=bvu=\dfrac {n\sum uv-\sum u\sum v}{n\sum u^2-(\sum u)^2}=\dfrac {4(19.5)-(0)(-0.5)}{4(20)-(0)^2}=0.975$

Regression equation of y on x is $y-\overline y=byx(x-\overline x)$ is

$$Y – 7.875 = 0.975 (x - 5)$$

$$Y = 0.975x + 3$$

When $x = 9$

$$Y = 0.975 (9) + 3$$

$$ = 11.775$$

Maintenance cost for a car 9 years old is $11.775 \times 1000 = 11775$ units

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