Problem:
In ongoing economic 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 199 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 income, 1999 per capita income xy
x (in $1000s) y (in 1000s)
7.9 22.9 180.91
10.4 27.8 289.12
8.7 25.9 225.33
8.7 23.4 203.58
9.3 27.4 198.9
7.6 22.1 167.96
9.7 25.7 249.29
11.1 33.9 376.29
8.4 22.1 185.64
9.4 26.1 246.28
10.9 30.3 330.27
9.1 22.3 202.93
11.8 30.4 358.72
10.2 27.4 279.48
What is the value of the slope of the least - squares regression line for these data? Round your answer to at least two decimal places.