Question

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg).

x 27 43 31 47 23 40 34 52
y 30 20 25 13 29 17 21 14

Complete parts (a) through (d), given Σx = 297, Σy = 169, Σx2 = 11,737, Σy2 = 3861, Σxy = 5845, and r ≈ −0.944.

(a) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx =

Σy =

Σx2 =

Σy2 =

Σxy =

r =

(b) Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x=

y=

ŷ = + x

(c) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =

explained = %

unexplained = %

(d) Suppose a car weighs x = 40 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)

= mpg

Homework Answers

Answer #1

ΣX = 297
ΣY = 169
ΣX * Y = 5845
ΣX2 = 11737
ΣY2 = 3861

Part a)



r = -0.944

part b)

X̅ = Σ( Xi / n ) = 297/8 = 37.12
Y̅ = Σ( Yi / n ) = 169/8 = 21.12


Equation of regression line is Ŷ = a + bX


b = -0.604
a =( Σ Y - ( b * Σ X) ) / n
a =( 169 - ( -0.6037 * 297 ) ) / 8
a = 43.536
Equation of regression line becomes Ŷ = 43.5358 - 0.6037 X.

part c)

Coefficient of Determination
= 0.891
Explained variation = 0.891* 100 = 89.1%
Unexplained variation = 1 - 0.891* 100 = 10.9%

part d)

When X = 40
Ŷ = 43.536 + -0.604 X
Ŷ = 43.536 + ( -0.604 * 40 )
Ŷ = 19.38

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 30 44 33 47 23 40 34 52 y 33 21 22 13 29 17 21 14 Complete parts (a) through (e), given Σx = 303, Σy = 170, Σx2 = 12,123, Σy2 = 3950, Σxy = 6040, and r ≈ −0.853. (a) Draw...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 27 43 29 47 23 40 34 52 y 31 18 27 13 29 17 21 14 Complete parts (a) through (e), given Σx = 295, Σy = 170, Σx2 = 11,617, Σy2 = 3950, Σxy = 5794, and r ≈ −0.951. (a) Draw...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 27 46 30 47 23 40 34 52 y 30 20 25 13 29 17 21 14 Complete parts (a) through (e), given Σx = 299, Σy = 169, Σx2 = 11,943, Σy2 = 3861, Σxy = 5880, and r ≈ −0.923. (b) Verify...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 25 46 32 47 23 40 34 52 y 29 20 23 13 29 17 21 14 Complete parts (a) through (e), given Σx = 299, Σy = 166, Σx2 = 11,963, Σy2 = 3706, Σxy = 5781, and r ≈ −0.932. (c) Find...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 28 42 29 47 23 40 34 52 y 30 17 24 13 29 17 21 14 Complete parts (a) through (e), given Σx = 295, Σy = 165, Σx2 = 11,587, Σy2 = 3701, Σxy = 5650, and r ≈ −0.945. (a) Draw...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x2544344723403452 y3017271329172114 Complete parts (a) through (e), given Σx = 299, Σy = 168, Σx2 = 11,915, Σy2 = 3854, Σxy = 5816, and r ≈ −0.943. (a) Draw a scatter diagram displaying the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola...
Please show formulas in excel Do heavier cars really use more gasoline? Suppose a car is...
Please show formulas in excel Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 29 46 33 47 23 40 34 52 y 29 22 24 13 29 17 21 14 Complete parts (a) through (e), given Σx = 304, Σy = 169, Σx2 = 12,244, Σy2 = 3837, Σxy = 6045, and...
Let x be the age in years of a licensed automobile driver. Let y be the...
Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 39% of all fatal accidents of 17-year-olds are due to speeding. x 17 27 37 47 57 67 77 y 39 22 22 12 10 7 5 Complete parts (a) through (e), given Σx = 329, Σy = 117, Σx2 = 18,263, Σy2 =...
Let x be the age of a licensed driver in years. Let y be the percentage...
Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way. x 37 47 57 67 77 87 y 5 8 10 14 33 46 Complete parts (a) through (e), given Σx =...
Let x be the age in years of a licensed automobile driver. Let y be the...
Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 37% of all fatal accidents of 17-year-olds are due to speeding. x 17 27 37 47 57 67 77 y 37 23 18 12 10 7 5 Complete parts (a) through (e), given Σx = 329, Σy = 112, Σx2 = 18,263, Σy2 =...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT