Sec. 7.4 COEFFICIENTS OF LINEAR CORRELATION 225 



4. In the formula of the previous problem, take 2(j/ 2 ) = 100 and plot the 

 left member of this equation on the vertical scale against r on the horizontal 

 scale. Take r from — 1 to +1 by increments of 0.2. 



5. Reynolds, Bond, and Kirkland (USD A Tech. Bull. 861) give the following 

 information on the relation between the cost of hauling logs and the length of 

 the haul in miles over high-grade dirt or gravel roads: 



Compute a coefficient of linear correlation between length of haul and cost per 

 1000 cubic feet of volume, and draw conclusions. Is this really a proper use of 

 correlation analysis? Would a regression analysis be better? 



6. The persons mentioned in problem 5 gave the following data on the cost 

 of producing 1000 cubic feet of hardwood logs in relation to the breast-high 

 diameter of the logs: 



Diam. (in.): 10 11 12 13 14 15 16 17 



Cost ($): 12.70 12.63 12.38 12.03 11.62 11.32 11.10 10.84 



Diam. (in.): 18 19 20 21 22 23 24 25 



Cost($): 10.63 10.49 10.40 10.28 10.13 10.04 9.96 9.88 



Make a scatter diagram of these data, compute r, and discuss it in terms of the 

 scatter diagram. Given: Sx 2 = 340; 2XF = 3019.59; ^{y 2 ) = 14.3129. 



Ans. r = —.97. 



7. Compute s y . x and sy for the data of problem 5, with Y = cost per 1000 cubic 

 feet. 



8. Calculate as in problem 7 for the data of problem 6. 



Ans. s y . x = 0.23; s Y = 0.98. 



9. The Yearbook of Labour Statistics for 1943-1944 gives the following average 

 daily wages of Chilean copper workers, in pesos: 



Year: 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 

 Wage: 11.89 11.26 11.75 11.33 12.80 13.31 14.77 16.37 21.31 23.20 25.34 



2(xy) = 155.74; 2F = 173.33; 2(F) 2 = 2996.1887. 



Construct a scatter diagram of these data, calculate sy and s y . x , and discuss their 

 sizes relative to the graph. 



10. Compute r for the data of problem 9 — ignoring the fact that the year is 

 not a random variable — and relate the size of the r to the appearance of the 

 scatter diagram. Let X = 1 for 1929, 2 for 1930, etc. Ans. r = +.91. 



11. Estimate the average wage for the year 1940 from the data of problem 9, 

 using r in the computation of the standard deviation of this estimate. 



