okay can someone set this up for me and help me understand it please.I tried it but i am clueless please show me how to solve this?
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.†
"e"= this symbol i willuse to represet that weird E for correlatlion
n=10 "e" x^2 = 93205
"e" x = 965 "e"xy=9165.10
"e"y = 95.3 "e"y^2= 920.47
a) find an equation of the least square line.
I used the equation that goes like this: r = (10 (9165.10)-(965)(95.3))/sqrt 10(93205)- (965)^2 - sqrt 10(920.47) - (95.3)^2
and what i came up with was -0.986 but then this would be for high correlation.
b)If the trend continues,how many banks will there be in 2004?
c) Find and interpret the coefficient of correlation?
To solve this problem, we will use the method of least squares to find the equation of the line that best fits the given data points.
a) To find the equation of the least squares line, we need to calculate the slope (b) and the y-intercept (a). The formula for the slope is given by:
b = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)
Using the given values n = 10, Σ(xy) = 9165.10, Σx = 965, Σy = 95.3, and Σ(x^2) = 93205, we can substitute these values into the formula:
b = (10(9165.10) - 965(95.3)) / (10(93205) - (965)^2)
Calculating this gives b ≈ -0.000422.
Next, we can calculate the y-intercept (a) using the formula:
a = (Σy - bΣx) / n
Substituting the values, we get:
a = (95.3 - (-0.000422)(965)) / 10
Calculating this gives a ≈ 98.409.
Therefore, the equation of the least squares line is y ≈ -0.000422x + 98.409.
b) To find the number of banks in 2004, we need to substitute x = 2004 into the equation of the least squares line:
y = -0.000422(2004) + 98.409
Calculating this will give you the predicted number of banks in 2004.
c) The coefficient of correlation (r) can be calculated using the formula:
r = (nΣ(xy) - ΣxΣy) / sqrt((nΣ(x^2) - (Σx)^2)(nΣ(y^2) - (Σy)^2))
Substituting the given values, we can calculate r.
Interpreting the coefficient of correlation:
- If the coefficient of correlation (r) is close to 1, it indicates a strong positive correlation.
- If r is close to -1, it indicates a strong negative correlation.
- If r is close to 0, it indicates no correlation or weak correlation.
In this case, since you obtained a value of -0.986, it suggests a strong negative correlation between the number of banks and the years since 1900. This means that as the years increase, the number of banks tends to decrease.