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In a study of the legibility and visibility of highway signs, a Pennsylvania res

ID: 3065894 • Letter: I

Question

In a study of the legibility and visibility of highway signs, a Pennsylvania research firm determined the maximum distance (in feet) at which each of 30 drivers could read a newly designed sign. The 30 participants were volunteers and ranged in age from 18 to 82 years old. The government agency that funded the research hoped to improve highway safety for older drivers and wanted to examine the relationship between age and the sign legibility distance. A scatterplot of the data is shown below. The sample correlation coefficient is r=0.801r=0.801 and the least-squares regression line is

y =576.683.01xy^=576.683.01x

Information

Driver age (years) and the maximum distance at which a highway sign was read (feet) for a volunteer sample of 30 drivers.

a). Match the correct descriptor to each component of describing the scatterplot.

Unusual observations

Direction

Form

Strength

Linear

Not present

Present

Non-linear

Strong

Positive

Weak

Negative

b). Calculate the coefficient of determination. Write your answer as a percentage (include the % symbol as units) and round to one decimal place.

c). Which of the following is a correct interpretation of the slope of the regression line?

The predicted maximum distance at which a highway sign is read for an individual that is zero years in age is -3.01.

A one foot increase in the maximum distance at which a highway sign was read is associated with a 3.01 year decrease in predicted age.

About 3.01% of the variability in maximum distances at which a highway sign was read can be explained by changes in age.

A one year increase in age is associated with a 3.01 feet decrease in the predicted maximum distance at which a highway sign was read.

d). Use the regression line to calculate the maximum distance at which a 5-year-old child could read the highway sign. Round your answer to 2 decimal places.

Unusual observations

Direction

Form

Strength

1.

Linear

2.

Not present

3.

Present

4.

Non-linear

5.

Strong

6.

Positive

7.

Weak

8.

Negative

Explanation / Answer

y =576.683.01xy^=576.683.01x

y^ predicted distance

x--age

Unusual observations--not present

Direction--negative

Form--linear

strength--strong

Solutionb:

r2=r..r=0.801*0.801= 0.641601

0.641601*100=64.2%

ANSWER:64.2%

Solutionc:

slope=-3.01

distance/age=-3.01

For unit increase in age,predicted distance decreases by 3.01

A one year increase in age is associated with a 3.01 feet decrease in the predicted maximum distance at which a highway sign was read.

Solutiond:

y =576.683.01xy^=576.683.01x

y^=576.683.01*(5)

y^= 561.63

ANSWER:561.63

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