Sec. 7.1 SCATTER DIAGRAMS AND TREND LINES 197 



sponding Y is necessarily about 40 units larger than if X — 5 because 

 there is definitely a downward trend of F as X increases. If the X 

 were ignored, all that observed difference of 40 units must be as- 

 signed to errors of measurement and/or to sampling accidents when, 

 in fact, only about one unit should be so assigned. Methods will be 

 presented later on in this chapter by which the apparent variation 

 among the F's can be reduced by taking account of the statistical 

 relation between X and Y. However, nothing extensive will be done 

 with non-linear trends. 



PROBLEMS 



1. Construct a scatter diagram for the following pairs of measurements, and 

 draw in by eye a straight line which seems to you to best depict the trend of 

 Y with X. Is the assumption that Y and X are linearly related a good one in 

 your opinion? 



2. From the following sampling data estimate how much Y changes, on the 

 average, for each unit increase in X. 



X: 36 43 50 40 42 45 40 45 39 48 



Y: 1.35 1.70 1.90 1.55 1.65 1.80 1.63 1.75 1.60 1.93 



Ans. About 0.04. 



3. Make a scatter diagram of the following pairs of observations and draw 

 in a freehand line to summarize the way Y changes with X: 



X, Y: 1,1; 2,2.5; 34-5; 4,6.0; 5.10.0; 6,14.5; 7,23.0; 8,35.0. 



4. Would you approve of the assumption that the carotene and the nitrogen- 

 free extract contents of pasture grasses are linearly related if assured that the 

 following pairs of such values form a representative sample for pasture grasses 

 of a given sort? Justify your decision. 



5. The following are means and corresponding standard deviations obtained 

 from samples of 10 observations, each drawn from an approximately normal popu- 

 lation. Construct a scatter diagram and decide what, if any, relationship exists 

 between the sampling mean and standard deviation from a normal population if 

 these samples are representative of such populations. Plot x on the horizontal axis. 



x 



58.4 6.04 53.4 10.33 63.0 9.33 60.4 11.40 



55.7 9.61 60.9 12.64 52.9 6.13 61.2 6.45 



62.0 6.70 56.7 8.03 58.1 8.15 67.7 10.21 



61.7 11.40 55.0 11.51 53.6 9.83 56.4 5.81 



54.0 10.52 59.3 9.05 57.8 10.92 54.4 10.78 



59.0 11.09 54.1 8.75 60.0 8.17 62.8 8.43 



