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Calculating the Least-Squares Regression Line Answers

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The line of best fit is also called the least-squares regression line. Which statement best explains that name?

A
The line is located on a scatterplot so that it minimizes the squared distances from the points to the line.
B
The line represents the place on the scatterplot that connects the points in the smallest square possible.
C
The line is located on a scatterplot so that it maximizes the squared distances from the points to the line.
D
The line represents the place on the scatterplot that crosses through the greatest number of points.
2
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⇒ 1.8

Answer:

1.8

3

21 ✔ 352112

A
21
B
✔ 35
C
2112
4

The table shows the number of cars sold per day at a dealership during a promotional sale.

Question illustration
Answer:

0.1

5

The table shows the number of kilograms a newborn pig weighs during its first week.

Question illustration
Answer:

0.96

6

The table shows the horsepower and top speeds of a variety of boat motors.

Answers:
ŷ = + x:21.12
ŷ = + x:0.14
According to the regression equation, a boat motor that has 100 horsepower is predicted to have a top speed of about miles per hour.:35
7

The table shows the weight and gas mileage of several vehicles.

Answers:
ŷ = + x:64.6
ŷ = + x:-20.2
According to the regression equation, a car that weighs 1.8 tons would have a gas mileage of about miles per gallon.:28
8

Let x represent the paper 1 score (out of 40) and ŷ represent the predicted paper 2 score (out of 100). Which correctly states the equation for the least-squares regression line and the interpretation of its slope?

A
ŷ = 5.2 + 2.2x; scoring 1 more point on paper 1 is associated with a 2.2-point increase on paper 2.
B
ŷ = 5.2 + 2.2x; scoring 2.2 more points on paper 1 is associated with a 1-point increase on paper 2.
C
ŷ = 2.2 + 5.2x; scoring 1 more point on paper 1 is associated with a 5.2-point increase on paper 2.
D
ŷ = 2.2 + 5.2x; scoring 5.2 more points on paper 1 is associated with a 1-point increase on paper 2.
9

Let x represent the points allowed and ŷ represent the predicted wins. Which correctly states the equation for the least-squares regression line and the interpretation of its y-intercept?

A
ŷ = 0.02 ‒ 14.92x; A team that allows 0.02 points is predicted to have about 0 wins.
B
ŷ = 0.02 ‒ 14.92x; A team that allows 0 points is predicted to have about 0.02 wins.
C
ŷ = 14.92 ‒ 0.02x; A team that allows 15 points is predicted to have about 0 wins.
D
ŷ = 14.92 ‒ 0.02x; A team that allows 0 points is predicted to have about 15 wins.
10

Question text not available

Answer:

0.50

11

The table shows the production budgets and worldwide gross revenues of eight 2018 films. Which statement gives the correct value and interpretation of r?

A
As budgets increased, the gross revenue increased; r = 0.38.
B
For every budget increase of $1 billion, gross revenue increased $0.38 billion; r = 0.38.
C
As budgets increased, the gross revenue increased; r = 0.62.
D
For every budget increase of $1 billion, gross revenue increased $0.62 billion; r = 0.62.
12

⇒ 0.18

Answer:

0.18

13

✔ 0.140.86 21.12

A
✔ 0.14
B
0.86
C
21.12
14

✔ -20.220.2 64.6

A
✔ -20.2
B
20.2
C
64.6
15

✔ 2896 101

A
✔ 28
B
96
C
101
16

The table shows the weight and gas mileage of several vehicles.

Answers:
ŷ = + x:64.6
ŷ = + x:-20.2
According to the regression equation, a car that weighs 1.8 tons would have a gas mileage of about miles per gallon.:28

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