Question

each of Exercises 14.98 - 14.103. a. compute SST, SSR, and SSE, using Formula 14.2 on page 641. The formulae for SST, SSR, and SSE are SST = Xn i=1 y2 i ?? ( Pn i=1 yi)2 n SSR = [ Pn i=1 xiyi ?? ( Pn i=1 xi Pn i=1 yi) =n]2 Pn i=1 x2i ?? ( Pn i=1 xi)2 =n SSE = SST ?? SSR; respectively. b. compute the coecient of determination, r2. c. determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. d. state how useful the regression equation appears to be for making predictions. 14.102 Crown-Rump Length. Following are the data on age and crown-rump length for fetuses from Exercise 14.62. Space Space Space x 10 10 13 13 18 19 19 23 25 28 y 66 66 108 106 161 166 177 228 235 280

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	10	66	100	4356	660
	10	66	100	4356	660
	13	108	169	11664	1404
	13	106	169	11236	1378
	18	161	324	25921	2898
	19	166	361	27556	3154
	19	177	361	31329	3363
	23	228	529	51984	5244
	25	235	625	55225	5875
	28	280	784	78400	7840
Total	178	1593	3522	302027	32476

Now sample size: n = 10

And

(b)

The coefficient of determination is:

c)

99.5% of variation in the observed values of the response variable explained by the regression.

It is equal to r-sqaure.

d)

Slope of the regression equation is

and intercept of the equation will be

So the regression equation will be

y'=-48.1284+11.6533x