Timothy Judge and Daniel Cable reported the results of a study demonstrating a n

Question

Timothy Judge and Daniel Cable reported the results of a study demonstrating a negative relationship between weight and income for a group of women professionals. [Dudge, T. A., & Cable, D. M. (2010). When it comes to pay, do the thin win? The effect of weight on pay for men and women. Journal of Applied Psychology, 96, 95-112. doi: 10.1037/a0020860] Following are data similar to those obtained in the study. To simplify the weight variable, the women are classified into five categories that measure actual weight relative to height, from 1 thinnest to 5 heaviest. Income figures are annual income (in thousands of dollars), rounded to the nearest $1,000 Income (Y) 115 78 53 63 37 Weight (X) 41 51 Compute the Pearson correlation. (Use two decimal places for the SS and SP values, three for r) Ex2 SSy SP 30 ] 660-900

Explanation / Answer

calculation procedure for correlation

sum of (x) = x = 30

sum of (y) = y = 660

sum of (x^2)= x^2 = 116

sum of (y^2)= y^2 = 49566

sum of (x*y)= x*y = 1619

to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)

covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1

= 1619 - [ 10 * (30/10) * (660/10) ]/10- 1

= -36.1

and now to calculate r( x,y) = -36.1/ (SQRT(1/10*1619-(1/10*30)^2) ) * ( SQRT(1/10*1619-(1/10*660)^2)

=-36.1 / (1.61*24.51)

=-0.91

value of correlation is =-0.91

coeffcient of determination = r^2 = 0.83

properties of correlation

1. If r = 1 Corrlation is called Perfect Positive Corrlelation

2. If r = -1 Correlation is called Perfect Negative Correlation

3. If r = 0 Correlation is called Zero Correlation

& with above we conclude that correlation ( r ) is = -0.9138< 0, perfect nagative correlation

( X) ( Y) X^2 Y^2 X*Y 1 115 1 13225 115 1 78 1 6084 78 4 53 16 2809 212 3 63 9 3969 189 5 37 25 1369 185 2 84 4 7056 168 5 41 25 1681 205 3 51 9 2601 153 1 94 1 8836 94 5 44 25 1936 220

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