Question

6 minutes. For each age group shown in the table, the median distance walked Two hundred and eighty boys completed a test that measures the distance that the boy can walk on a flat, hard surface by the boys that age group is given. Median Six-Minute Walk Distance (meters) Representative Age (Midpoint of Age Group) Age Group 3-5 4.0 543.3 585.0 6-8 7.0 9-11 10.0 666.3 12-15 13.5 702.1 17.0 16-18 728.6 (c) 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 -8.54 7,0 -12.141 26.869 10.0 10.04 13.5 -16.174 17.0

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
4	543.3	39.69	10355.10	641.09
7	585	10.89	3607.20	198.20
10	666.3	0.09	451.14	-6.37
13.5	702.1	10.24	3253.56	182.53
17	728.6	44.89	6978.93	559.72

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	51.5	3225.3	105.8	24645.9	1575.16
mean	10.30	645.06	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   10.30   ,     ȳ = Σy/n =   645.06  
                  
SSxx =    Σ(x-x̅)² =    105.8000          
SSxy=   Σ(x-x̅)(y-ȳ) =   1575.2          
                  
estimated slope , ß1 = SSxy/SSxx =   1575.2   /   105.800   =   14.8881
                  
intercept,   ß0 = y̅-ß1* x̄ =   491.7127          
                  
so, regression line is   Ŷ =   491.712665   +   14.888091   *x

c)

X					Ŷ	residual,ei=y-yhat
4					551.27	-7.965
7					595.93	-10.929
10					640.59	25.706
13.5					692.70	9.398
17					744.81	-16.210