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Regression of maintenance cost on car age

Short answer

Regression equation: ŷ = −1.70 + 4.45X (cost in Rs.000). For a 10-year-old car, estimated maintenance cost = 42.80 (Rs.000).

The following table gives the age of the cars of a certain company and annual maintenance costs: Age of cars (Years): 2 4 6 8 10 Maintenance costs (Rs.000): 10 15 22 32 46 Obtain the regression equation for cost related to age and also estimate the cost of maintenance for 10 yrs old car.

Let X = age of car (years) and Y = annual maintenance cost (Rs. 000). Regression of cost on age: Ŷ = a + bX.

Sums (n = 5):

        x        y       xy       x²       y²
        2       10       20        4      100
        4       15       60       16      225
        6       22      132       36      484
        8       32      256       64     1024
       10       46      460      100     2116
---------------------------------------------
       30      125      928      220     3949

Σx = 30, Σy = 125, Σxy = 928, Σx² = 220, Σy² = 3949

Means: x̄ = 6.0000, ȳ = 25.0000

Sxx = Σx² − (Σx)²/n = 40.0000 Sxy = Σxy − (Σx)(Σy)/n = 178.0000 Syy = Σy² − (Σy)²/n = 824.0000

Slope b = Sxy/Sxx = 178.0000/40.0000 = 4.4500 Intercept a = ȳ − bx̄ = 25.0000 − (4.4500)(6.0000) = -1.7000

Regression equation: Ŷ = -1.70 + 4.45 X (r = 0.980)

Cost for a 10-year-old car

Ŷ = -1.7000 + 4.4500 × 10 = 42.80 (Rs. 000)

Answer: Ŷ = -1.70 + 4.45X; maintenance cost for a 10-year-old car ≈ Rs. 42800 (the fitted value; the actual observed cost is Rs. 46,000).

✓ Answer checked by Claude Sonnet 5.5

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