City government has collected the following data on annual sales tax collections
ID: 1092692 • Letter: C
Question
City government has collected the following data on annual sales tax collections and new car registrations:
Y: Annual Sales Tax Collections ($ millions)
X: New Car Registrations
(thousands)
1.0
10
1.4
12
1.9
15
2.0
16
2.1
17
2.3
20
(a) Determine the least squares regression equation.
(b) Using the results of part (a), find the estimated sales tax collections if new car registrations total 22.
Y: Annual Sales Tax Collections ($ millions)
X: New Car Registrations
(thousands)
1.0
10
1.4
12
1.9
15
2.0
16
2.1
17
2.3
20
Explanation / Answer
So, the regression equation is:
Annual Sales Tax = -0.20885+0.132813*New Car Registrations
b) estimated sales tax collections if new car registrations total 22:
Annual Sales Tax = -0.20885+0.132813*22
=$2.713 million
SUMMARY OUTPUT Regression Statistics Multiple R 0.974675 R Square 0.949991 Adjusted R Square 0.937489 Standard Error 0.121888 Observations 6 ANOVA df SS MS F Significance F Regression 1 1.128906 1.128906 75.98598 0.000954 Residual 4 0.059427 0.014857 Total 5 1.188333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.20885 0.233895 -0.89294 0.422356 -0.85825 0.440543 -0.85825 0.440543 X Variable 1 0.132813 0.015236 8.716994 0.000954 0.09051 0.175115 0.09051 0.175115