Question 83418
The following data are from a survey in which x represents 
the years since 1900 and y corresponded to the number of 
banks, in thousands, in the United States.†
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n=10 the weird E(x^2) = 93,205 ;
E(x) = 965 ; E(xy) = 9165.10
E(y) = 95.3 ;E(y^2) = 920.47 
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a. Find an equation of the least squares line.
y-hat = bo + b1x
bo = [(E(y)(E(x^2)-(E(x))(E(xy))] / [nE(x^2) )- (E(x))^2]
bo = [95.3*93.205-965*9165.1] / [10*93.205-965^2]
bo = [-8835439.064] / [-30292.95] = 9.49748...
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b1 = [nE(xy) -E(x)*E(y)] / [nE(x^2) - (Ex)^2]
b1 = [10*9165.1 - 965*95.3] / [ 10*93.205 - 965^2]
b1 = [-313.5] / [ -930292.95]
b1 = 0.00033699
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y-hat = 9.49748 + 0.00033699 x
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b. If the trend continues, how many banks will there be in
2004?
From 1900 to 2004 is 104 years
Letting x = 104 you get:
# of banks in 2004 = 9.49748 + 0.0033699(104) = 9.84 thousand banks
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Cheers,
Stan H.