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. Age Group Representative Age (Midpoint of Age Group) Median Six-Minute Walk Distance (meters) 3–5 4 544.3 6–8 7 584.0 9–11 10 667.3 12–15 13.5 701.1 16–18 17 727.6 This experiment also reported the 6-minute walk distances (in meters) for 248 girls age 3 to 18 years. The median 6-minute walk distances for girls for the five age groups, respectively, were 494.4 580.3 657.8 655.6 662.9.

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

(d)

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

Representative Age (x)	Residual (meters)
4
7
10
13.5
17

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

ŷ = ____ + (_____)x

The researchers decided to use a curve rather than a straight line to describe the relationship between median distance walked in 6 minutes and age for girls. What aspect of the residual plot supports this decision?

A.The decision to use a curve is supported by the clear negative linear pattern in the residual plot.

B.The decision to use a curve is not supported by the residual plot as there are no unusual patterns.    

C. The decision to use a curve is supported by the clear positive linear pattern in the residual plot.

D.The decision to use a curve is supported by the clear curved pattern in the residual plot.

E.The decision to use a curve is supported by the outliers in the residual plot.

Answer 1

C) Equation of regression line :

y = a + b*x

We need to find the sums ∑x , ∑y, ∑x*y, ∑x²

We have n = 5 , ∑x =51.5 , ∑y =3051, ∑x*y=32737.6, ∑x² = 636.25

b is slope = =  

b = 12.404

a is intercept =

= = 3051 / 5 = 610.2

= = 51.5/ 5 = 10.3

a = = 610.2 - (0.872*10.3)

a = 482.443

Therefore regression line ,

ŷ = 482.443+12.404*x

(d) Compute the five residuals.

Residuals = y - ŷ

We can find ŷ using equation of regression line for all x values

Residual plot

So D.The decision to use a curve is supported by the clear curved pattern in the residual plot.