Data from the U.S. Federal Reserve Board on the percentage of disposable persona

Question

Data from the U.S. Federal Reserve Board on the percentage of disposable personal income required to meet consumer loan payments and mortgage payments for selected years are shown in the following table. What is the value of the correlation coefficient for this data set? (Give the answer to four decimal places.)

r=

Detailed solution please. I am very lost, based on the books example.

Consumer
Debt Household
Debt Consumer
Debt Household
Debt 7.89 6.23 6.25 5.72 7.91 6.15 6.08 5.94 7.64 5.94 6.33 6.10 7.61 5.84 6.98 6.29 7.48 5.84 7.37 6.08 7.48 5.86 7.53 5.80 7.37 5.81 7.85 5.82 6.56 5.78

Explanation / Answer

r( X,Y) =    Co V ( X,Y) / S.D (X) * S.D (y)                      
r( X,Y) =    Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )                        
                          
Co v ( X, Y ) =   1 /15 (644.4307) - [ 1/15 *108.33 ] [ 1/15 *89.2] =            0.015          
S. D ( X ) =   Sqrt( 1/15*787.8117-(1/15*108.33)^2)           0.603          
S .D (Y) =    Sqrt( 1/15*530.8892-(1/15*89.2)^2)           0.173          
r(x,y) =    0.015 / 0.603*0.173   =   0.1438              
                          
If r = 0.1438> 0 ,Positive Correlation                          
                          
Coeffcient of determination = r^2 = 0.0207                          

( X) ( Y) X^2 Y^2 X*Y 7.89 6.23 62.2521 38.8129 49.1547 7.91 6.15 62.5681 37.8225 48.6465 7.64 5.94 58.3696 35.2836 45.3816 7.61 5.84 57.9121 34.1056 44.4424 7.48 5.84 55.9504 34.1056 43.6832 7.48 5.86 55.9504 34.3396 43.8328 7.37 5.81 54.3169 33.7561 42.8197 6.56 5.78 43.0336 33.4084 37.9168 6.25 5.72 39.0625 32.7184 35.75 6.08 5.94 36.9664 35.2836 36.1152 6.33 6.1 40.0689 37.21 38.613 6.98 6.29 48.7204 39.5641 43.9042 7.37 6.08 54.3169 36.9664 44.8096 7.53 5.8 56.7009 33.64 43.674 7.85 5.82 61.6225 33.8724 45.687 108.33 89.2 787.8117 530.8892 644.4307 Totals

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