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
a) Scatter plot:
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)
A data set is given below. (a) Draw a scatter diagram. Comment on the type of...
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The scatter diagram for the data set below is shown. (a) Given that x overbar equals 2.5 commax=2.5,s Subscript x Baseline equals 2.258318 commasx=2.258318,y overbar equals 4.083 commay=4.083,s Subscript y Baseline equals 2.1046773 commasy=2.1046773,and r equals negative 0.9530761 commar=−0.9530761,determine the least-squares regression line. (b) Graph the least-squares regression line on the scatter diagram. -16-38xy A scatter diagram has a horizontal x-axis labeled from negative 1 to 6 in increments of 1 and a vertical y-axis labeled from negative 3 to...
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