CarWeight (lbs) Miles per Gallon3,765Car 119Car 23,96417Car 33,47021Car 43,17522Car 52,58027Car 63,73018Car 72,60526Car 83,772173,310Car 920Car 102,99125Car 112,75226An engineer wanted to determine how the weight of a car affects gas mileage. The accompanying datarepresent the weights of various domestic cars and their gas mileages in the city for a certain model year.Suppose that we add Car 12 to the original data. Car 12 weighs 3 comma 3053,305 pounds and gets1919 miles per gallona) Compute the linear correlation coefficient with Car 12 included.The linear correlation coefficient with Car 12 included is r-?(Round to three decimal places as needed.)b) Recompute the linear correlation coefficient with Car 13 included. How did this new value affect yourresult?The linear correlation coefficient with Car 13 included is r-?t) Why does this observation not follow the pattern of the data?

Question
Asked Sep 8, 2019
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Car
Weight (lbs) Miles per Gallon
3,765
Car 1
19
Car 2
3,964
17
Car 3
3,470
21
Car 4
3,175
22
Car 5
2,580
27
Car 6
3,730
18
Car 7
2,605
26
Car 8
3,772
17
3,310
Car 9
20
Car 10
2,991
25
Car 11
2,752
26
An engineer wanted to determine how the weight of a car affects gas mileage. The accompanying data
represent the weights of various domestic cars and their gas mileages in the city for a certain model year.
Suppose that we add Car 12 to the original data. Car 12 weighs 3 comma 3053,305 pounds and gets
1919 miles per gallon
a) Compute the linear correlation coefficient with Car 12 included.
The linear correlation coefficient with Car 12 included is r-?
(Round to three decimal places as needed.)
b) Recompute the linear correlation coefficient with Car 13 included. How did this new value affect your
result?
The linear correlation coefficient with Car 13 included is r-?
t) Why does this observation not follow the pattern of the data?
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Car Weight (lbs) Miles per Gallon 3,765 Car 1 19 Car 2 3,964 17 Car 3 3,470 21 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,730 18 Car 7 2,605 26 Car 8 3,772 17 3,310 Car 9 20 Car 10 2,991 25 Car 11 2,752 26 An engineer wanted to determine how the weight of a car affects gas mileage. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Suppose that we add Car 12 to the original data. Car 12 weighs 3 comma 3053,305 pounds and gets 1919 miles per gallon a) Compute the linear correlation coefficient with Car 12 included. The linear correlation coefficient with Car 12 included is r-? (Round to three decimal places as needed.) b) Recompute the linear correlation coefficient with Car 13 included. How did this new value affect your result? The linear correlation coefficient with Car 13 included is r-? t) Why does this observation not follow the pattern of the data?

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Expert Answer

Step 1

Enter the data as shown in excel

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A B 1 car Miles Per gallon weight 2 1 3765 19 3 2 3964 17 4 3470 21 5 4 3175 22 6 5 2580 27 7 6 3730 18 7 2605 26 9 8 3772 17 10 3310 11 10 2991 25 2752 12 11 26 13 12 3053 19 14 nON N

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Step 2

Apply the following formula in excel and click enter

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A B Miles Per gallon 1 weight car 2 1 3765 19 3 2 4 3 3964 17 3470 21 5 4 3175 22 6 5 2580 27 7 6 3730 18 8 7 2605 26 9 8 3772 17 10 9 3310 20 11 10 2991 25 12 11 2752 26 13 12 3053 19 =CORREL(B2:B13, C2:C13) 14 st

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Step 3

The correlation after adding car 12 is...

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A Miles Per gallon 1 car weight 2 1 3765 19 3 2 3964 17 4 3470 21 5 4 3175 22 6 5 2580 27 7 6 3730 18 7 2605 26 9 8 3772 17 10 3310 20 11 10 2991 25 12 11 2752 26 13 12 3053 19 14 0.91696946 TY

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