Question

A data set is given

a)

(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y.

​(b) Given that

x overbarxequals=3.83333.8333​,

s Subscript xsxequals=2.40142.4014​,

y overbaryequals=3.98333.9833​,

s Subscript ysyequals=1.74521.7452​,

and

requals=negative 0.9457−0.9457​,

determine the​ least-squares regression line.

​(c) Graph the​ least-squares regression line on the scatter diagram drawn in part​ (a).

x	0	2	4	5	6	6
y	6.0	5.8	4.7	3.0	2.1	2.3

Answer 1

(a) SCATTER DIAGRAM

Line of Regression Y on X i.e Y = bo + b1 X
					X	Y	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
0	6	14.694	4.067	-7.731
2	5.8	3.361	3.3	-3.331
4	4.7	0.028	0.514	0.119
5	3	1.361	0.967	-1.147
6	2.1	4.695	3.547	-4.081
6	2.3	4.695	2.833	-3.647

calculation procedure for regression
mean of X = sum ( X / n ) = 3.8333
mean of Y = sum ( Y / n ) = 3.9833
sum ( (Xi - Mean)^2 ) = 28.834
sum ( (Yi - Mean)^2 ) = 15.23
sum ( (Xi-Mean)*(Yi-Mean) ) = -19.818
b1 = sum ( (Xi-Mean)*(Yi-Mean) ) / sum ( (Xi - Mean)^2 )
= -19.818 / 28.834
= -0.687
bo = sum ( Y / n ) - b1 * sum ( X / n )
bo = 3.9833 - -0.687*3.8333 = 6.618
value of regression equation is, Y = bo + b1 X
least-squares regression line = Y'=6.618-0.687* X          

(c) Regression line on the graph