The table shows the number of a particular brand of luxury cars sold in various

Question

The table shows the number of a particular brand of luxury cars sold in various years. Identify the polynomial model for the number of cars sold in a given year since 2000 and use the model to estimate the number of cars sold in 2005. P(x) = -38.23x^3 + 56.86x^2 + 1098.23x + 557.48 The estimated number of cars sold in 2005 was 2691. P(x) = 6.04x^4 - 111.18x^3 + 329.04x^2 + 787.26x + 588.97 The estimated number of cars sold in 2005 was 2626 P(x) = -38.23x^3 + 56.86x^2 + 1098.23x + 557.48 The estimated number of cars sold in 2005 was 3413 P(x) = 6.04x^4 - 135.32x^3 + 698.78x^22 - 228.48x + 247.95 The estimated number of cars sold in 2005 was 3432

Explanation / Answer

Answer D

For polynomial regression with Y = ax^4 + bX^3 + c x^2 + d X + e

We can estimate the paramaters with Year 0 = 2000, Year 1 = 2001 and so on.

So Year 5 = 2005

So after solving for regression and finding values

or we can test for different polynomials

The last column shows correct regression and the values.

7

So The estimated value in 2005 is 3432.

0 557.48 588.97 247.95 1 1674.34 1600.13 588.97 2 2675.54 2686.85 1600.19 3 3331.7 3399.49 2687.13 4 3413.44 3433.37 3400.27 5 2691.38 2628.77 3435.05 6 936.14 970.93 2631.87

7

-2081.66 -1409.95 976.09

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