in ongoing economic analyses, the federal government compares per capita incomes

Question

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 about the 1999 per capita income for a state (denoted by from its 1980 per capita income we have gotten information (denoted by following bivariate data the per capita income (in thousands of dollars) for a sample of fineen state in the years 1980 and 1999 Economic Analysis, Survey of current Business, May 2000). The data are plotted in the scatter (source: Us. Bureau of plot in Figure 1

Explanation / Answer

We will find an equation of the regression line in 4 steps.

Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=145.6 , Y=411.3 , XY=4048.25 , X2=1435.72

Step 3: Use the following equations to find a and b:

By substituting the above values in below formula's we get a and b

a = YX2XXY/nX2(X)2=3.229

therefore a = 3.229

b = nXYXY/nX2(X)2=2.492

therefore b = 2.492

Step 4: Substitute a and b in regression equation formula

y  = a + bx

y = 3.229 + 2.492x

Therefor from the above least squares regression line

slope = 2.49 and

y intercept = 3.23

X Y XY XX 9.9 30.9 305.91 98.01 11.1 33.9 376.29 123.21 9.4 26.2 246.28 88.36 9.4 26.1 245.34 88.36 8.5 23.4 198.9 72.25 12 29.8 357.6 144 10.2 28.7 292.74 104.04 11.8 30.4 358.72 139.24 8.7 25.9 225.33 75.69 8.7 23.4 203.58 75.69 7.9 22.9 180.91 62.41 10.8 31.7 342.36 116.64 9.7 29.7 288.09 94.09 9.3 27.4 254.82 86.49 8.2 20.9 171.38 67.24

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