Question 83418: Decrease in Banks The number of banks in the United
States has dropped about 30% since 1992. 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.†
n=10 the weird E symbol x^2 = 93,205
werid E x = 965 weird E xy = 9165.10
weird y = 95.3 weird y^2 = 920.47
a. Find an equation of the least squares line.
b. If the trend continues, how many banks will there be in
2004?
c. Find and interpret the coefficient of correlation.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.†
----------
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
-------------
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...
---------
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
-----------
y-hat = 9.49748 + 0.00033699 x
----------------------------------
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.
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