Below is the data on the fuel consumption y of a car at various speeds x . Fuel

Question

Below is the data on the fuel consumption y of a car at various speeds x. Fuel consumption is measured in liters of gasoline per 100 kilometers driven, and speed is measured in kilometers per hour. Software tells us that the equation of the least-squares regression line is

Using this equation we can add the residuals to the original data. (Data set may be found here.)

(c) Give the value of the first residual, for x = 10. Your calculation should be based on your results from your software or calculator (slope to 5 decimal places, and intercept to 3 decimal places), and thus you should be able to provide higher accuracy than that provided in the table, which contains rounding errors. (Round your answer to three decimal places.)

  

What is the sum of residuals in the table? What would be the answer if we had performed an exact calculation for the residuals, without the roundoff errors present in the table?

exact sum

Explanation / Answer

c)

yhat= 11.058-0.01466*x

when, x= 10

yhat= =11.058-0.01466*10

yhat= 10.911

error = predicted-original = yhat-y = 10.911-21

=10.911-21

-10.089

sum from table:

=(10.09+2.24-0.62-2.47-3.33-4.28-3.73-2.94-2.17-1.32-0.42-0.57+1.64+2.76+ 3.97)/15

-0.076667

excat sum

0

residuals are normally distributed with mean 0 and constant variance

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