What is the value of the sample correlation coefficient for these data?

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Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. (If necessary, consult a list of formulas.)

 

What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.
 
 
 
 
In ongony cconomic analyses, the federal government compares per capita incomes not only among different states but also for the same state at different
times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy.
Would we have gotten information about the 1999 per capita income for a state (denoted by y) from its 1980 per capita income (denoted by x)? The following
bivariate data give the per capita income (in thousands of dollars) for a sample of sixteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic
Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1. Also given are the products of the 1980 per capita incomes
and 1999 per capita incomes for each of the sixteen states. (These products, written in the column labelled "xy," may aid in calculations.)
1980 per capita 1999 per capita
income, x
income, y
ху
(in $1000s)
(in $1000s)
New Hampshire
9.9
30.9
305.91
Alabama
7.9
22.9
180.91
38+
North Dakota
23.5
190.35
8.1
36-
Hawaii
11.5
27.8
319.7
34+
Illinois
11.1
31.3
347.43
32+
Montana
9.1
22.3
202.93
30+
Virginia
10.2
29.5
300.9
28+
Vermont
8.7
25.9
225.33
26+
Kansas
10.0
26.6
266
24-
Louisiana
8.8
22.8
200.64
22+
Rhode Island
9.7
29.7
288.09
20-
Utah
8.5
23.4
198.9
Idaho
8.7
23.4
203.58
to
Техas
10.0
26.5
265
Figure 1
Missouri
9.4
26.2
246.28
Pennsylvania
10.2
28.7
292.74
Transcribed Image Text:In ongony cconomic analyses, the federal government compares per capita incomes not only among different states but also for the same state at different times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy. Would we have gotten information about the 1999 per capita income for a state (denoted by y) from its 1980 per capita income (denoted by x)? The following bivariate data give the per capita income (in thousands of dollars) for a sample of sixteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1. Also given are the products of the 1980 per capita incomes and 1999 per capita incomes for each of the sixteen states. (These products, written in the column labelled "xy," may aid in calculations.) 1980 per capita 1999 per capita income, x income, y ху (in $1000s) (in $1000s) New Hampshire 9.9 30.9 305.91 Alabama 7.9 22.9 180.91 38+ North Dakota 23.5 190.35 8.1 36- Hawaii 11.5 27.8 319.7 34+ Illinois 11.1 31.3 347.43 32+ Montana 9.1 22.3 202.93 30+ Virginia 10.2 29.5 300.9 28+ Vermont 8.7 25.9 225.33 26+ Kansas 10.0 26.6 266 24- Louisiana 8.8 22.8 200.64 22+ Rhode Island 9.7 29.7 288.09 20- Utah 8.5 23.4 198.9 Idaho 8.7 23.4 203.58 to Техas 10.0 26.5 265 Figure 1 Missouri 9.4 26.2 246.28 Pennsylvania 10.2 28.7 292.74
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