A taxicab company owns a large fleet of taxicabs. The cost per mile of operating

Question

A taxicab company owns a large fleet of taxicabs. The cost per mile of operating a cab is believed to be influenced by its age. 10 cabs were selected, and a careful study was made to determine the operating cost per mile of each cab. The data are as follows: (n 10) 2. Cab Cab Cab Cab Cab Cab Cab Cab Cab Cab SUMS 8 9 10 Y=Cost/mile(cents)| 10.1 11.4 11.7 12 12 13.2 13.7 13.8 14 15.2 | )=127.1 x-Age-months 3 7 8 9 10 14 16 19 27 36132=149 The estimates of bo and bi are: Variable Coefficients Std. Error 0.3375 Sbo Intercept = bo Slope b 110.6178 0.3375-Sbo 0.140420.01904 Si Using a T- Test, test whether the slope term is significantly different from zero. That is, test Ho: ,-0, vs Ha: 1 * 0 at .05. (2-tailed test).

Explanation / Answer

2)a)

TS = 0.14042/0.01904 = 7.373585

df = n-2 = 8

p-value = 2 P(t > 7.3758) = 0.000078 << 0.05

hence we reject the null and comclude that b1 is significant

2b) df_reg = 1 , df_error = n-2

MS = SS/df

F = MS_reg/MS_Residual

SS_Total = sum Y_i^2 - n (Y_bar)^2 = 20.829

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df SS MS F Significance F Regression 1 18.15732012 18.15732012 54.36974772 7.81483E-05 Residual 8 2.671679878 0.333959985 Total 9 20.829

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