Calculating the Least-Squares Regression Line…

1

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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

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.

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%

A

ŷ = 4.317 + 0.310x

B

ŷ = 0.310 + 4.317x

C

ŷ = –14.71 + 1.585x

D

ŷ = 1.585 – 14.71x

3

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%

A

8.10 pretzels

B

10.83 pretzels

C

18.58 pretzels

D

75.95 pretzels

4

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

5

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

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.

6

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?

A

0.68

B

0.83

C

0.91

D

0.95

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, what is the equation for the least-squares regression line?

A

ŷ = 3.79 – 0.10x

B

ŷ = 0.10 + 3.79x

C

ŷ = 16.15 – 3.28x

D

ŷ = –3.28 + 16.15x

8

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?

A

–0.56

B

–0.10

C

0.10

D

0.56

Calculating the Least-Squares Regression Line Answers

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