Question

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

Answer 1

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