Two hundred and eighty boys completed a test that measures the distance that the

Question

Two hundred and eighty boys completed a test that measures the distance that the subject can walk on a flat, hard surface in 6 minutes. For each age group shown in the table, the median distance walked by the boys in that age group is also given.

(b) Find the equation of the least-squares regression line that describes the relationship between median distance walked in 6 minutes and representative age. (Round your values to three decimal places.)

(c) Compute the five residuals. (Round your answers to three decimal places.)

Age Group Representative
Age (Midpoint
of Age Group) Median Six-Minute
Walk Distance
(meters) 3–5 4 544.3 6–8 7 583.0 9–11 10 666.3 12–15 13.5 701.1 16–18 17 726.6

Explanation / Answer

Result:

(b) Find the equation of the least-squares regression line that describes the relationship between median distance walked in 6 minutes and representative age. (Round your values to three decimal places.)

The regression line

Walk distance =492.500+14.734*age

Regression Analysis

r²

0.947

n

5

r

0.973

k

1

Std. Error

20.599

Dep. Var.

Walk Distance

ANOVA table

Source

SS

df

MS

F

p-value

Regression

22,968.2845

1  

22,968.2845

54.13

.0052

Residual

1,272.9275

3  

424.3092

Total

24,241.2120

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

492.4995

22.5906

21.801

.0002

420.6062

564.3928

Age

14.7340

2.0026

7.357

.0052

8.3608

21.1073

(c) Compute the five residuals. (Round your answers to three decimal places.)

Observation

Walk Distance

Predicted

Residual

1

544.300

551.436

-7.136

2

583.000

595.638

-12.638

3

666.300

639.840

26.460

4

701.100

691.409

9.691

5

726.600

742.978

-16.378

Regression Analysis

r²

0.947

n

5

r

0.973

k

1

Std. Error

20.599

Dep. Var.

Walk Distance

ANOVA table

Source

SS

df

MS

F

p-value

Regression

22,968.2845

1  

22,968.2845

54.13

.0052

Residual

1,272.9275

3  

424.3092

Total

24,241.2120

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

492.4995

22.5906

21.801

.0002

420.6062

564.3928

Age

14.7340

2.0026

7.357

.0052

8.3608

21.1073

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