For Problem #4.38, assume a = -0.158 and b = 0.1308. Then, find an estimate for

Question

For Problem #4.38, assume a = -0.158 and b = 0.1308. Then, find an estimate for the tax collections if new car registrations total 22,000. State the answer in dollars.

ANNUAL SALES TAX COLLECTIONS IN MILLIONS) NEW CAR REGISTRATIONS (IN THOUSANDS) 1.0 1.4 1.9 2.0 1.8 2.1 2.3 10 12 15 16 14 17 20 Determine the following: a) The least-squares regression equation. b) Using the results of part (a), find the estimated sales tax collec- tions if new car registrations total 22.000. c) The coefficients of correlation and determination .Px

Explanation / Answer

Annual sales tax collection (in millions)-(Y) New car registration (in thopusands) - (X) XY X2 Y2 1 10 10 100 1 1.4 12 16.8 144 1.96 1.9 15 28.5 225 3.61 2 16 32 256 4 1.8 14 25.2 196 3.24 2.1 17 35.7 289 4.41 2.3 20 46 400 5.29 Total 194.2 1610 23.51 a= -0.158 b = 0.1308 Then regression equation will be Y = a + b X Y = -0.158 + 0.1308 (X) Given X = 22000 menas 22 then Y =? Y = -0.158 + 0.1308 (22) Y = 2.7196 millions Coeff of Correlation r = Sum of XY / sqrt of (sum of X2 X sumof y2) r = 194.2 / sqrt of (1610 X 23.51) r = 0.998 Coeff of determination = square of r = r2 R = (0.998)2 = 0.996

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