232 LINEAR REGRESSION AND CORRELATION Ch. 7 



mean = 10 bushels per acre, with the standard deviation = s = 13 bushels per 

 acre. Is one variety superior to the other or not? Give reasons for answer. 



Arts, t S 3.00; UD/F, P S .01. 



15. Suppose that a large number of tractor gears has been produced and that 

 90 per cent of them are classifiable as acceptable. If a sample of 10 gears is 

 taken at random from this group, which of the following is more likely to 

 occur? (a) The sample will contain less than 90 per cent "acceptable" and 

 will, therefore, give a pessimistic picture of the quality of the whole batch. 

 Or (b) the sample will contain at least 90 per cent "acceptable" and hence 

 will, if anything, overestimate the quality of the batch. 



16. The depth of deterioration (in inches) is used as an index of the mer- 

 chantable volume of timber remaining in fire-killed Douglas fir. Kimmey and 

 Furniss (USDA Tech. Bull. 851) report a study made in western Oregon and 

 Washington on such timber. The following data on old-growth trees were read 

 from one of their graphs: 



Years after fire: 

 Depth in inches: 



Years after fire: 

 Depth in inches: 



What do you conclude from a regression analysis is the average increase in 

 depth of deterioration per decade? Given ZXF = 5123.0, 2F 2 = 1617.09. 



Ans. 3.0 inches = point estimate; CI 95 : 0.25-/3^0.35. 



17. Economists sometimes speak of commodities with elastic or inelastic 

 prices, meaning generally that a commodity which is slow to change price in 

 the face of changes in demand has an elastic price. If you adjust prices for 

 inflation and for depression, and if demand is measured by per capita consump- 

 tion of a given commodity, the definition of an elastic, or inelastic, price can 

 be made more specific. For example, if the slope of the linear trend line re- 

 lating adjusted price (F) to consumption per capital (X) is less than unity, 

 the price can be called elastic. If /3 is greater than 1, the price then is called 

 inelastic. Given the following data regarding whole milk and cream, would 

 the price be classified as elastic according to the above definition after due 

 allowance for sampling error? 



Adjusted price 



($/cwt) 1.88 2.06 2.07 2.26 2.36 2.29 2.48 2.19 



Consumption 



per capita (cwt) 3.43 3.50 3.72 3.93 4.12 4.32 4.20 4.00 



18. In the preceding problem a definition of an elastic price was based upon 

 the size of the regression coefficient, /3. What information would it add to 

 this discussion to include the size of the correlation coefficient? 



19. Following are adjusted farm beef prices (per hundredweight) and con- 

 sumption per capita (hundredweight) for the 10-year period indicated: 



Year: 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 



Price: 6.67 6.67 7.52 7.79 8.32 8.63 8.62 7.94 8.71 9.06 

 Con- 

 sump- 

 tion: 0.55 0.54 0.54 0.55 0.60 0.61 0.53 0.55 0.59 0.61 



