Calculating the Least-Squares Regression Line

Question 1

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

Revolt · Accepted Answer

The line is located on a scatterplot so that it minimizes the squared distances from the points to the line.

Question 2

Question 3

Revolt · Accepted Answer

35

Question 3

The table shows the number of cars sold per day at a dealership during a promotional sale. What is the equation of the least-squares regression line, where is the predicted number of cars sold and x is the day? Round each coefficient or constant to the nearest tenth. = + x

Revolt · Accepted Answer

0.1; 1.8

Question 4

The table shows the number of kilograms a newborn pig weighs during its first week. What is the equation of the least-squares regression line, where is the predicted weight and x is the day? Round each coefficient or constant to the nearest hundredth. = + x

Revolt · Accepted Answer

0.96; 0.18

Question 5

The table shows the horsepower and top speeds of a variety of boat motors. What is the equation of the least-squares regression line, where ŷ is the predicted top speed and x is the horsepower? ŷ = + x According to the regression equation, a boat motor that has 100 horsepower is predicted to have a top speed of about miles per hour.

Revolt · Accepted Answer

21.12; Selection 1: 21.12; Selection 2: 0.14; Selection 3: 35

Question 6

The table shows the weight and gas mileage of several vehicles. What is the equation of the least-squares regression line, where ŷ is the predicted gas mileage and x is the weight? ŷ = + x According to the regression equation, a car that weighs 1.8 tons would have a gas mileage of about miles per gallon.

Revolt · Accepted Answer

64.6; Selection 1: 64.6; Selection 2: -20.2; Selection 3: 28

Question 7

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?

Revolt · Accepted Answer

ŷ = 5.2 + 2.2x; scoring 1 more point on paper 1 is associated with a 2.2-point increase on paper 2.

Question 8

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?

Revolt · Accepted Answer

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

Question 9

Question 10

Revolt · Accepted Answer

160165

Question 10

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

Revolt · Accepted Answer

As budgets increased, the gross revenue increased; r = 0.62.

Calculating the Least-Squares Regression Line Answers

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