Calculating the Least-Squares Regression Line…

1

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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 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

2

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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?

A

–0.56

B

–0.10

C

0.10

D

0.56

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

ŷ = 4.317 + 0.310x

B

ŷ = 0.310 + 4.317x

C

ŷ = –14.71 + 1.585x

D

ŷ = 1.585 – 14.71x

4

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class. The results are displayed in the scatterplot.

A

passes through each data point.

B

minimizes the sum of the squared residuals.

C

maximizes the sum of the squared residuals.

D

is least able to make accurate predictions for the data.

5

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

6

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%

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.

7

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

0.521

B

0.547

C

0.722

D

0.740

8

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

–0.82

B

–0.68

C

0.68

D

0.82

9

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

10

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 equation for the least-squares regression line?

A

ŷ = 180.2 + 0.68x

B

ŷ = 0.68 + 180.2x

C

ŷ = –124.1 + 1.22x

D

ŷ = 1.22 – 124.1x

Calculating the Least-Squares Regression Line Answers

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