Square Footage and Sales The table shows the total square foot ages (in billions

Question

Square Footage and Sales The table shows the total square foot ages (in billions) of retailing space at shopping centers and their sales (in billions of dollars) for 11 years. The equation of the regression line is y = 445.257x - 1480.117. (Adapted from International Council for shopping Centers) Trees The table shows the heights (in feet) and trunk diameters (in inches) of eight trees. The equation of the regression line is y = 0.479x - 24.086. State and Federal Government Wages The table shows the average weekly wages (in dollars) for slate government employees and federal government employees for 10 years. The equation of the regression line is y = 1.632x - 200.284. (Source: U.S Bureau of Labor statistics)

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=615 , Y=102.2 , XY=7937.6 , X2=47447

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

a=YX2XXY/nX2(X)2

  =102.2(47447)615(7937.6)/847447615224.086

b=nXYXY/nX2(X)2=8(7937.6)615(102.2)/847447(615)20.479

Step 4: Substitute a and b in regression equation formula

y = a + bx= 24.086 + 0.479x

slope=0.479

y intercept=-24.086

X Y XY XX 70 8.3 581 4900 72 10.5 756 5184 75 11 825 5625 76 11.4 866.4 5776 85 14.9 1266.5 7225 78 14 1092 6084 77 16.3 1255.1 5929 82 15.8 1295.6 6724

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