The data set below compares the fuel consumption y of a car to the speed it is d

Question

The data set below compares the fuel consumption y of a car to the speed it is driven at 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

ˆy=11.0580.01466x

Blue

Pink

Yellow

Would you use the regression line to predict y from x?

Yes

No

Maybe

Choose the correct explanations for you previous answer from the list below.

The scatterplot shows behaviour that is markedly non-linear.

Although the points are scattered relative to the regression line, the regression line always gives us a good prediction.

r2

is very close to zero, thus the prediction accuracy is very low.

Since the regression always satisfies facts 2, 3, and 4, it always supplies a reliable prediction.

r2

is very close to zero, thus ensuring a high prediction accuracy.

r2

is very close to one, thus the prediction accuracy is very low.

Verify the value of the first residual, for x = 90. 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.
Answer to 3 decimal places.

Speed x Fuel used y Residual Speed x Fuel used y Residual 21.00 13.00 10.00 8.00 7.00 5.90 6.30 6.95 10.09 2.24 -0.62 -2.47 3.33 -4.28 -3.73 -2.94 10 90 100 110 120 130 140 150 7.57 8.27 9.03 9.87 10.79 -0.42 0.57 1.64 2.76 3.97 40 50 60 12.83 80

Explanation / Answer

Make a scatterplot of the observations and draw the regression line on your plot. Which of the following regression lines is the correct one?

Answer: Yellow

Would you use the regression line to predict y from x?

Answer: Yes

Choose the correct explanations for you previous answer from the list below.

Answer: The scatterplot shows behaviour that is markedly non-linear. Although the points are scattered relative to the regression line, the regression line always gives us a good prediction.

Verify the value of the first residual, for x = 90. 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.
Answer to 3 decimal places.

Answer : -2.169 (Regression line y=11.0580.01466x)

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