AnswersCA-Statistics and Probability ACalculating the Least-Squares Regression Line

Calculating the Least-Squares Regression Line Answers

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A statistics student wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students.Using technology, what is the correlation?

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A
–0.56
B
–0.10
C
0.10
D
0.56
2
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The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-14.714.3171.6890.046Handspan1.5850.3105.1140.000S = 3.05R-Sq = 52.1%R-Sq(Adj) = 51.7%

Question illustration
A
8.10 pretzels
B
10.83 pretzels
C
18.58 pretzels
D
75.95 pretzels
3

A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table.Using technology, what is the correlation coefficient?

Question illustration
A
0.68
B
0.83
C
0.91
D
0.95
4

A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table.Using technology, the slope of the least-squares regression line is

Question illustration
A
0.68, which means for each additional point in the English score, the math score is predicted to increase by 0.68 points.
B
0.68, which means for each additional point in the math score, the English score is predicted to increase by 0.68 points.
C
1.22, which means for each additional point in the English score, the math score is predicted to increase by 1.22 points.
D
1.22, which means for each additional point in the math score, the English score is predicted to increase by 1.22 points.
5

A statistics student is studying if there is a relationship between the price of a used car and the number of miles it had been driven. She collects data for 20 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.PredictorCoefSE Coeft-ratiopConstant24157.22164.12.9650.046Mileage-0.1810.0245.3770.000S = 3860.7R-Sq = 68.0%R-Sq(Adj) = 67.5%

A
$22,347.20
B
$23,917.20
C
$24,157.20
D
$25,967.20
6

A statistics student wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students.Using technology, what is the equation for the least-squares regression line?

Question illustration
A
ŷ = 3.79 – 0.10x
B
ŷ = 0.10 + 3.79x
C
ŷ = 16.15 – 3.28x
D
ŷ = –3.28 + 16.15x
7

A statistics student wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected students.Using technology, the y-intercept is

Question illustration
A
4.5, which means a student with no absences has a GPA of 4.5.
B
4.5, which means a student with no absences is predicted to have a GPA of 4.5.
C
3.79, which means a student with no absences is predicted to have a GPA of 3.79.
D
3.79, but it does not make sense to interpret the y-intercept in this context.
8

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%

Question illustration
A
arm span, foot length will increase by about 0.186 cm.
B
foot length, arm span will increase by about 0.186 cm.
C
arm span, foot length is predicted to increase by about 0.186 cm.
D
foot length, arm span is predicted to increase by about 0.186 cm.
9

The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-14.714.3171.6890.046Handspan1.5850.3105.1140.000S = 3.05R-Sq = 52.1%R-Sq(Adj) = 51.7%

Question illustration
A
pretzel, the handspan will increase by about 1.585 cm.
B
pretzel, the handspan is predicted to increase by about 1.585 cm.
C
centimeter in handspan, the number of pretzels increases by about 1.585.
D
centimeter in handspan, the number of pretzels is predicted to increase by about 1.585.
10

A certain standardized test measures students’ knowledge in math and English. The scatterplot displays the scores for 10 randomly selected students.

Question illustration
A
is least able to make accurate predictions for the data.
B
makes the sum of the squared residuals as large as possible.
C
makes the sum of the squared residuals as small as possible.
D
causes the relationship between English scores and math scores to be strongest.

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