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Simple Linear Regression — Test Answers

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1
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Using technology, what is the slope of the least-squares regression line and what is its interpretation?

A
The slope is 1 point 9 8 , which means for each additional inch in height, the child’s weight will increase by 1 point 9 8 pounds.
B
The slope is 0 point 5 0 , which means for each additional pound in weight, the child’s height is predicted to increase by 0 point 5 inches.
C
The slope is 0 point 5 0 , which means for each additional pound in weight, the child’s height will increase by 0 point 5 inches.
D
The slope is 1 point 9 8 , which means for each additional inch in height, the child’s weight is predicted to increase by 1 point 9 8 pounds.
2
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Which scatterplot represents the student data?

A
Image with description A scatter plot 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).
B
Image with description A scatter plot 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).
C
Image with description A scatter plot 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).
D
Image with description A scatter plot 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).
3

The equation hat y is equal to 17 point 4 plus 0 point 5 x is called the least-squares regression line because it

A
makes the strongest association between weight and height.
B
is least able to make accurate predictions for the data.
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.
4

What effect does the circled point have on the slope and y - intercept of the least-squares regression line?

A
This point will increase the value of the slope and increase the value of the y - intercept.
B
This point will decrease the value of the slope and increase the value of the y - intercept.
C
This point will decrease the value of the slope and decrease the value of the y - intercept.
D
This point will increase the value of the slope and decrease the value of the y - intercept.
5

Which of the following is an accurate description of the scatterplot?

A
The kickers have unusually high success rates when the distance is small.
B
As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
C
As the distance of the attempt increases, the kickers have a lower success rate for their field goals.
D
The kickers have unusually low success rates when the distance is large.
6

The equation of the least-squares regression line is hat y is equal to 68 point 5 plus 11 point 4 x , where hat y is the number of students enrolled and x is number of years the school has been open. Which shows the residual plot?

A
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 20 and ends at 15 with equal intervals of 5, such as negative 20, negative 15, negative 10, negative 5, 0, 5, 10, and 15. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, negative 12; 1 dot at 2, negative 3; 1 dot at 3, 3; 1 dot at 4, 10; 1 dot at 5, 12; 1 dot at 6, 6, 1 dot at 7, 1; and 1 dot at 8, -16.
B
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 15 and ends at 20 with equal intervals of 5, such as negative 15, negative 10, negative 5, 0, 5, 10, 15, and 20. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, 12; 1 dot at 2, 3; 1 dot at 3, negative 3; 1 dot at 4, negative 10; 1 dot at 5,negative 12; 1 dot at 6, negative 6, 1 dot at 7, negative 1; and 1 dot at 8, 16.
C
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 80 and ends at 20 with equal intervals of 20, such as negative 80, negative 60, negative 40, negative 20, 0, and 20. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, 18; 1 dot at 2, 16; 1 dot at 3, 10; 1 dot at 4, 5; 1 dot at 5, negative 2; 1 dot at 6, negative 22, 1 dot at 7, negative 39; and 1 dot at 8, negative 70.
D
Image with description A dot plot with the x axis titled Number of years begins with 0 and ends at 8 with equal intervals of 2, such as 0, 2, 4, 6, and 8. The y axis titled Residual begins with negative 20 and ends at 80 with equal intervals of 20, such as negative 20, 0, 20, 40, 60, and 80. A horizontal line parallel to the x axis starts from the point where y is 0. There is 1 dot at approximately 1, negative 18; 1 dot at 2, negative 16; 1 dot at 3, negative 10; 1 dot at 4, negative 5; 1 dot at 5, 5; 1 dot at 6, 22, 1 dot at 7, 38, and 1 dot at 8, 75.
7

Which is a true statement regarding Springside?

A
Springside strengthens the correlation shown in the scatterplot.
B
Removing Springside would increase the value of the correlation coefficient.
C
Springside weakens the correlation shown in the scatterplot.
D
Springside does not affect the correlation.
8

Based on the scatterplots, what type of model is most appropriate for comparing distance and temperature?

A
A power model is appropriate because the scatterplot relating ln(distance) to ln(temperature) is roughly linear.
B
A linear model is appropriate because the scatterplot relating ln(distance) to ln(temperature) is roughly linear.
C
An exponential model is appropriate because the scatterplot relating distance to ln(temperature) is roughly linear.
D
An exponential model is appropriate because the scatterplot relating distance to temperature is curved.
9

What is the equation of the least-squares regression line?

A
the natural log of widehat Element is equal to negative 0 point 1 0 1 plus 2 point 3 0 5 times Time
B
the natural log of widehat Element is equal to 2 point 3 0 5 minus 0 point 1 0 1 times Time
C
widehat Element is equal to 2 point 3 0 5 minus 0 point 1 0 1 ln Time
D
the natural log of widehat Time is equal to negative 0 point 1 0 1 plus 2 point 3 0 5 times Element
10

Based on the scatterplots, which type of model is most suitable for estimating the stock price?

A
A power model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.
B
An exponential model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.
C
A linear model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship.
D
An exponential model is suitable because the scatterplot of weeks against log(stock price) shows a strong linear relationship.
11

How would the correlation change if the stopping distances were recorded in meters, rather than feet?

A
Since the points would be more spread out, the value of the correlation coefficient would decrease.
B
Since the number of meters would be less than the number of feet, the value of the correlation coefficient would decrease.
C
The value of the correlation coefficient would not change.
D
Since the number of meters would be less than the number of feet, the value of the correlation coefficient would increase.
12

Which statement regarding the association shown could explain the relationship?

A
Schools in less affluent areas tend to have smaller class sizes, which is associated with lower test scores.
B
Schools in more affluent areas have larger class sizes, which is associated with higher test scores.
C
Class size appears to have little effect on test scores.
D
Schools in more affluent areas have smaller class sizes, which is associated with higher test scores.
13

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. Open image in full-screen view Which of the following is the best interpretation of the coefficient of determination r squared ?

A
About 37 percent of the variation in arm span is accounted for by the linear relationship formed with the foot length.
B
About 63 percent of the variation in foot length is accounted for by the linear relationship formed with the arm span.
C
About 63 percent of the variation in arm span is accounted for by the linear relationship formed with the foot length.
D
About 65 percent of the variation in foot length is accounted for by the linear relationship formed with the arm span.
14

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 widehat y is equal to 0 point 0 8 x plus 1 point 2 0 , where x represents the number of pieces in a set and widehat y is the predicted price (in dollars) of the set. What is the predicted price of a set that has 2 comma 520 pieces?

A
2 dollars comma 017 point 2 0
B
3 dollars comma 024 point 0 8
C
31 dollars comma 485
D
202 point 8 0 dollars
15

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, the natural log of open paren widehat Fuel Efficiency close paren is equal to 1 point 4 3 7 plus 0 point 5 4 1 ln Speed , what is the fuel efficiency for a speed of 60 mph?

A
3 point 6 5 mpg
B
36 point 5 2 mpg
C
33 point 9 0 mpg
D
38 point 5 5 mpg
16

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation widehat y is equal to 4 point 9 x plus 15 point 2 , where x represents attendance (in thousands) and widehat y is the predicted number of wins. Which statement best describes the meaning of the slope of the regression line?

A
For each increase in the number of wins by 1 , the predicted attendance increases by 15 comma 200 .
B
For each increase in attendance by 1 comma 000 , the predicted number of wins increases by 15 point 2 .
C
For each increase in attendance by 1 comma 000 , the predicted number of wins increases by 4 point 9 .
D
For each increase in the number of wins by 1 , the predicted attendance increases by 4 comma 900 .
17

Water is poured into a large, cone-shaped cistern. The volume of water, measured in cm cubed , is reported at different time intervals, measured in seconds. The scatterplot of volume versus time showed a curved pattern. Which of the following would linearize the data for volume and time?

A
Seconds , cm cubed
B
the natural log of Seconds , cm cubed
C
Seconds , the natural log of open paren cm cubed close paren
D
the natural log of Seconds , the natural log of open paren cm cubed close paren
18

The owner of a used car dealership is trying to determine if there is a relationship between the price of a used car and the number of miles it has been driven. The owner collects data for 25 cars of the same model with different mileage and determines each car’s price using a used car website. The analysis is given in the computer output. Open image in full-screen view Using the computer output, what is the value of the coefficient of determination?

A
0 point 4 6
B
0 point 8 2
C
0 point 6 8
D
0 point 7 0
19

Based on data taken from airline fares and distances flown, it is determined that the equation of the least-squares regression line is hat y is equal to 102 point 5 0 plus 0 point 6 5 x , where start set hat y end set is the predicted fare and x is the distance, in miles. One of the flights was 350 miles and its residual was negative 105 point 0 0 What was the fare for this flight?

A
330 point 0 0 dollars
B
225 point 0 0 dollars
C
102 point 5 0 dollars
D
435 point 0 0 dollars
20

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 widehat y is equal to 0 point 0 8 x plus 1 point 2 0 , where x represents the number of pieces in a set and widehat y 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 dollars , the predicted number of pieces is 1 point 2 0 .
B
When the number of pieces is 0 , the predicted price is 1 point 2 0 dollars . This interpretation is not meaningful because a set cannot have 0 pieces.
C
When the number of pieces is 0 , the predicted price is 0 point 0 8 dollars . This interpretation is not meaningful because a set cannot have 0 pieces.
D
When the price of a set is 0 dollars , the predicted number of pieces is 0 .

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