Question

# Two hundred and eighty boys completed a test that measures the distance that the boy can...

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

Age Group Representative
Age (Midpoint
of Age Group)
Median Six-Minute
Walk Distance
(meters)
3–5 4.0 543.3
6–8 7.0 585.0
9–11 10.0 666.3
12–15 13.5 702.1
16–18 17.0 728.6

A

Find the equation of the least-squares regression line (the equation of the best fit line). (Round your values to three decimal places.)

ŷ = (____,_____)

B

Calculate the five residuals, make sure to use at least 5 decimals for the slope and intercept when calculating the predicted values and residuals. (Round your answers to three decimal places.)

Representative
Age (x)
Residual
4.0
7.0
10.0
13.5
17.0

Ans:

a)

 x y 1 4 543.3 2 7 585 3 10 666.3 4 13.5 702.1 5 17 728.6 mean 10.3 645.06 std. dev 5.142956 78.49511 r 0.975459 slope,b 14.88809 intercept,a 491.71267

Regression equation:

y'=14.888 x+491.713

b)

 x y y'=14.88809x+491.71267 residual=y-y' 4 543.3 551.26503 -7.965 7 585 595.9293 -10.929 10 666.3 640.59357 25.706 13.5 702.1 692.701885 9.398 17 728.6 744.8102 -16.210

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