Question

A data set is given below.

​(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=4.15004.1500​,

s Subscript ysyequals=1.51891.5189​,

and

requals=negative 0.9349−0.9349​,

determine the​ least-squares regression line.

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

x	00	22	44	55	66	66
y	5.85.8	5.95.9	4.74.7	3.23.2	2.52.5	2.82.8

​(a) Choose the correct graph below.

A.

0606xy

A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (0,0.2), (2,0.2), (4,1.4), (5,2.8), (6,3.6), (6,3.2). All vertical coordinates are approximate.

B.

0606xy

A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (0,2.6), (2,2.8), (4,3.2), (5,4.8), (6,5.8), (6,6). All vertical coordinates are approximate.

C.

0606xy

A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (5.8,0), (6,2), (4.8,4), (3.2,5), (2.6,6), (2.8,6). All horizontal coordinates are approximate.

D.

0606xy

A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (0,5.8), (2,6), (4,4.8), (5,3.2), (6,2.6), (6,2.8). All vertical coordinates are approximate.There appears to be

▼

relationship.​(b)

ModifyingAbove y with caretyequals=nothingxplus+left parenthesis nothing right parenthesis

​(Round to three decimal places as​ needed.)

​(c) Choose the correct graph below.

A.

0606xy

A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (0,5.8), (2,6), (4,4.8), (5,3.2), (6,2.6), (6,2.8). All vertical coordinates are approximate. A line falling from left to right passes through the points (1,5.8) and (6,2.8). All vertical coordinates are approximate. The line passes within 2 vertical units of all plotted points.

B.

0606xy

A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (0,5.8), (2,6), (4,4.8), (5,3.2), (6,2.6), (6,2.8). A line falling from left to right passes through the points (1,5.8) and (6,2.8). All vertical coordinates are approximate. The line passes within 1 vertical unit of all plotted points.

C.

0606xy

A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following six points are plotted, listed from left to right: (0,2.6), (2,2.8), (4,3.2), (5,4.8), (6,5.8), (6,6). A line rising from left to right passes through the points (0,2.6) and (6,6). All vertical coordinates are approximate. The line passes within 2 vertical units of all plotted points.

D.

0606xy

Answer 1

a) Scatter plot:

Scatterplot 7 6 5 4 > 3 .. 2 1 0 0 2 4 ch 8 X

b)

Slope, b = r*sy/sx = -0.9349*1.51888/2.40139 = -0.59133

Intercept, a = y̅ - b* x̅ = 4.15 - (-0.59133)*3.83333 = 6.41676

Regression equation :   

ŷ = 6.417 + (-0.591) x  

c)

Scatterplot 7 6 5 4 Y 3 N 1 0 0 2 4 ch 8 х