Question

X    y

992 , 155

2316 , 263     

532 , 163

493 , 246

2560 , 311

1823 , 336

745 , 143

4589 , 954

1354 , 203

906 , 173

1. Now, let’s calculate the least-squares line based on your data. Show your work. You can use the following table to assist you or you may use Excel if you are more comfortable with the software. *If you use Excel, you must submit the spreadsheet electronically on Blackboard. Hint: Use Guided Example 4 (p. 555) as a guide. Write your equation in the form, y=a+bx.

x	y	x2	xy	y2
x=	y=	x2=	xy=	y2=

1. x=
2. y=
3. b=
4. a=
5. y=

Answer 1

	x	Y	X2	Y2	XY
	992	155	984064	24025	153760
	2316	263	5363856	69169	609108
	532	163	283024	26569	86716
	493	246	243049	60516	121278
	2560	311	6553600	96721	796160
	1823	336	3323329	112896	612528
	745	143	555025	20449	106535
	4589	954	21058921	910116	4377906
	1354	203	1833316	41209	274862
	906	173	820836	29929	156738
Sum	16310	2947	41019020	1391599	7295591

Σx = 16310, Σy = 2947, Σx2 = 41019020, Σy2 = 1391599, Σxy = 7295591, n =10

b = (n*Σxy-ΣxΣy)/(nΣx2-(Σx)2) = (10*7295591-16310*2947)/(10*41019020-16310*16310) = 0.173

a = (Σy-a*Σx)/n = (2947-0.173*16310)/10 = 12.537

y = a+bx

y = 12.537 + 0.173x