The accompanying data were read from graphs that appeared in an article. The var

Question

The accompanying data were read from graphs that appeared in an article. The variables shown are the number of acres burned in forest fires in the western United States and timber sales. Year Number of Acres Burned (thousands) Timber Sales. Compute the correlation coefficient. (Give the answer to three decimal places.) Is there a correlation between timber sales and acres burned in forest fires? strong positive correlation weak positive correlation strong negative correlation weak negative correlation no correlation. The article concludes that "heavier logging led to large forest fires." Do you think this conclusion is justified based on the given data? Yes No

Explanation / Answer

Correlation.

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 /11 (24505.3) - [ 1/11 *3028 ] [ 1/11 *84.2] = 120.667                              
S. D ( X ) = Sqrt( 1/11*986108-(1/11*3028)^2) = 117.776                              
S .D (Y) = Sqrt( 1/11*768.6-(1/11*84.2)^2) = 3.359                              
r(x,y) = 120.667 / 117.776*3.359 = 0.305                              
                              
If r = 0.305> 0 ,weak Positive Correlation                              

( X) ( Y) X^2 Y^2 X*Y 198 2.2 39204 4.84 435.6 253 3.6 64009 12.96 910.8 263 4.5 69169 20.25 1183.5 386 6.8 148996 46.24 2624.8 72 9.7 5184 94.09 698.4 440 11.2 193600 125.44 4928 174 11.2 30276 125.44 1948.8 233 10.3 54289 106.09 2399.9 446 10 198916 100 4460 391 10.9 152881 118.81 4261.9 172 3.8 29584 14.44 653.6 3028 84.2 986108 768.6 24505.3 = TOTALS

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