AnswersDRHS GA-Statistical ReasoningR-squared and s

R-squared and s — Unit test Answers

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A popular social media platform has begun offering stock shares to the public. In the past 2 years, the price of the stock has generally increased. An investment specialist gathers data on the stock price during the past 2 years and creates an exponential model for estimating the stock price based on the number of weeks after the first public offering.

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A
$2.27 because ŷ = 0.0022(95) + 2.0583 = 2.2673.
B
$9.65 because and e2.2673 = 9.6533.
Option B
C
$185.05 because and 102.2673 = 185.05.
Option C
D
$220.44 because and 102.3433 = 220.44
Option D
2
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Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, , what is the fuel efficiency for a speed of 60 mph?

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A
3.65 mpg
B
33.90 mpg
C
36.52 mpg
D
38.55 mpg
3

Data was recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation, , what is the predicted temperature after 3 minutes?

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A
33.45 oC
B
62.24 oC
C
65.17 oC
D
66.69 oC
4

Market researchers were interested in the relationship between the number of pieces in a building-brick set and the cost of the set. The researchers collected information from a survey and used it to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of the set. What is the predicted price of a set that has 2,520 pieces?

A
$202.80
B
$2,017.20
C
$3,024.08
D
$31,485
5

College administrators at a small, private college noticed that students who had higher high school GPAs tend to have higher college GPAs.

A
Explanatory variable: size of collegeResponse variable: college GPA
B
Explanatory variable: high school GPAResponse variable: college GPA
C
Explanatory variable: college GPAResponse variable: high school GPA
D
Explanatory variable: type of college (private vs. public)Response variable: college GPA
6

How is the distance from the sun for planets in our solar system related to the mean temperature of each planet? To find out, scatterplots that relate the distance of each planet (including Pluto) from the sun in millions of miles and the mean planetary temperature in Kelvin were created. Some of the scatterplots use the natural log to transform one, or both, of the variables.

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A
An exponential model is appropriate because the scatterplot relating distance to temperature is curved.
B
A linear model is appropriate because the scatterplot relating ln(distance) to ln(temperature) is roughly linear.
C
A power model is appropriate because the scatterplot relating ln(distance) to ln(temperature) is roughly linear.
D
An exponential model is appropriate because the scatterplot relating distance to ln(temperature) is roughly linear.
7

The scatterplot illustrates the relationship between distance and success rate of field-goal attempts for a sample of football kickers.

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A
The kickers have unusually low success rates when the distance is large.
B
The kickers have unusually high success rates when the distance is small.
C
The kickers have higher success rates for longer field-goal attempts.
D
The kickers have lower success rates for longer field-goal attempts.
8

Based on data taken from airline fares and distances flown, it is determined that the equation of the least-squares regression line is ŷ = 102.50 + 0.65x, where ŷ is the predicted fare and x is the distance, in miles.

A
$102.50
B
$435.00
C
$225.00
D
$330.00
9

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of a set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. Which statement best describes the meaning of the y-intercept of the regression line?

A
When the price of a set is $0, the predicted number of pieces is 0.
B
When the price of a set is $0, the predicted number of pieces is 1.20.
C
When the number of pieces is 0, the predicted price is $1.20. This interpretation is not meaningful because a set cannot have 0 pieces.
D
When the number of pieces is 0, the predicted price is $0.08. This interpretation is not meaningful because a set cannot have 0 pieces.
10

The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis.Which of the following is the best interpretation of the coefficient of determination r2?

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A
About 37% of the variation in arm span is accounted for by the linear relationship formed with the foot length.
B
About 65% of the variation in foot length is accounted for by the linear relationship formed with the arm span.
C
About 63% of the variation in arm span is accounted for by the linear relationship formed with the foot length.
D
About 63% of the variation in foot length is accounted for by the linear relationship formed with the arm span.
11

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7%

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A
5.79 cm
B
22.15 cm
C
29.76 cm
D
29.80 cm
12

A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output.Which of the following represents the standard deviation of the residuals?

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A
1.223
B
34.55
C
78.712
D
124.13
13

Janice is considering buying a new home. She wants to estimate the monthly utilities (heating and air conditioning). She figures that the utilities are dependent on the size (square footage) of the home. She collects data on 10 homes in the neighborhood and finds a linear model to give the relationship between the size of the home and the monthly utilities. The equation of the line is ŷ = –8.1 + 1.91x, where ŷ is the mean monthly cost in utilities and x is the square footage of the home. The residual plot is shown.

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A
No, there is no clear pattern in the residual plot.
B
Yes, there is no clear pattern in the residual plot.
C
No, there are no homes between 2,300 and 2,900 square feet.
D
Yes, half of the residuals are positive and half are negative.
14

To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car’s stopping distance (in feet) for each volunteer. The value of r for the scatterplot is 0.935.

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A
The value of the correlation coefficient would not change.
B
Since the points would be more spread out, the value of the correlation coefficient would decrease.
C
Since the number of meters would be less than the number of feet, the value of the correlation coefficient would increase.
D
Since the number of meters would be less than the number of feet, the value of the correlation coefficient would decrease.
15

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7%

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A
0.630
B
0.649
C
0.794
D
0.806
16

A newspaper collected information on schools in its circulation area in order to compare their quality. Two measures the newspaper collected for each school, mean class size and mean score on a statewide reading exam, are shown in the scatterplot. One school in the report, Springside Elementary, is labeled in the graph.

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A
Springside does not affect the correlation.
B
Springside weakens the correlation shown in the scatterplot.
C
Springside strengthens the correlation shown in the scatterplot.
D
Removing Springside would increase the value of the correlation coefficient.
17

A sports analyst determines that the number of points scored in a basketball game is related to the number of shots taken during the game. The least-squares regression line is ŷ = 5.0 + 1.2x, where ŷ is the predicted number of points scored and x is the number of shots taken.

A
45
B
55
C
65
D
75
18

College administrators noticed that students who had higher high school GPAs tend to have higher college GPAs. The data in the table show various high school GPAs and college GPAs for a sample of students.

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A
A graph titled high school and college G P A has H S G P A on the x-axis, and College G P A on the y-axis. Points are at (3.25, 3.2), (3.5, 3.0), (3.5, 2.9), (3.25), (3.0), (2.5, 3.0), (4, 3.0), (4, 3.1), (3.5, 3.1), (3.25, 3.1), (3.25, 3.1), (3.5, 3.0), (3.5, 3.0), (4, 3.1), (3, 3.0), (3.5, 3.1), (2.25, 2.9), (2.5, 2.8).
Option A
B
A graph titled high school and college G P A has College G P A on the x-axis, and H S G P A on the y-axis. Points are at (2.8, 2.5), (2.9, 2.25), (2.9, 3.5), (3, 2.5), (3, 3), (3, 3.25), (3, 3.5), (3, 4), (3.1, 3.25), (3.1, 3.5), (3.1, 4), (3.2, 3.25).
Option B
C
A graph titled high school and college G P A has H S G P A on the x-axis, and College G P A on the y-axis. Points are at (3.25, 3.2), (3.5, 3.0), (3.5, 2.9), (3.25), (3.0), (2.5, 3.0), (4, 3.0), (4, 3.1), (3.5, 3.1), (3.25, 3.1), (3.25, 3.1), (3.5, 3.0), (3.5, 3.0), (4, 3.1), (3, 3.0), (3.5, 3.1), (2.25, 2.9), (2.5, 2.8), (4, 3.2).
Option C
D
A graph titled high school and college G P A has College G P A on the x-axis, and H S G P A on the y-axis. Points are at (2.8, 2.5), (2.9, 2.25), (2.9, 3.5), (3, 2.5), (3, 3), (3, 3.25), (3, 3.5), (3, 4), (3.1, 3.5), (3.1, 4), (3.2, 3.25).
Option D
19

The number of students enrolled at a school varies from year to year. For the first eight years the school is open, the number of students enrolled is recorded in the table shown.

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot.

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A
is least able to make accurate predictions for the data.
B
makes the strongest association between weight and height.
C
minimizes the sum of the squared distances from the actual y-value to the predicted y-value.
D
maximizes the sum of the squared distances from the actual y-value to the predicted y-value.

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