Question

In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Calculate the linear correlation coefficient. Round to three decimal places. Rainfall (in inches), 8 6.3 10.9 10 16.3 78 4.5 13.1 13.5 = Yield (bushels per acre), y 46.5 42.2 54.8 55 78.4 45.2 27.9 72 748 O A. 0.981 B. 0.900 OC 0.899 D. 0.998

Answer 1

We need to find the sums ∑x , ∑y, ∑x*y, ∑x² and ∑y²

х y 46.5 6.3 42.2 10.9 54.8 10 55 78.4 16.3 x² y? xty 64 2162.25 372 39.69 1780.84 265.86 118.81 3003.04 597.32 100 3025 550 265.69 6146.56 1277.92 60.84 2043.04 352.56 20.25 778.41 125.55 171.61 5184 943.2 182.25 5595.04 1009.8 1023.14 29718.18 5494.21 7.8 45.2 4.5 13.1 13.5 90.4 27.9 72 74.8 496.8 Total

∑x = 90.4 , ∑y = 496.8 , ∑x*y = 5494.21, ∑x² = 1023.14 and ∑y² = 29718.18

r = $\frac{n\sum (x*y)-\sum (x)*\sum (y)}{\sqrt{[n\sum x^2-(\sum x)^2 ]*[n\sum y^2-(\sum y)^2]}}$

r =

(9+ 5494.21)- (90.4$ 496.8) (90.4 + 90.41] * [9 * 29718.18)-(496.8 * 496.8)] [9+ 1023.14)

r = 4537.17 / 4625.902

r = 0.981