SOLUTION: 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
Algebra.Com
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
--------------
===============
Cheers,
Stan H.
RELATED QUESTIONS
In 1992, the population of the United States was about 249 million and the exponential... (answered by josgarithmetic)
The number of farms in the United States was 2.19 million in 2000. By 2006, the number... (answered by rfer)
The number of opera companies in the united states decreased from 97 in 1985 to to 89 in... (answered by robertb)
The Community banks are banks with less than a billion dollars of assets. The Community... (answered by ewatrrr)
Forty percent of banks did not earn profits during 2003. The SEC selects two banks at... (answered by stanbon)
In the United states 154,000,000 tons of garbage are produced annually. On an average,... (answered by josmiceli)
According to a Gallop poll, 27% of American adults have confidence in banks. Suppose that (answered by Boreal)
Solve. If necessary, round to the nearest tenth of a percent.
Data from the Federal... (answered by math_tutor2020)
. In 1985, 45 percent of a document storage facility’s 60 customers were banks, and in... (answered by longjonsilver)