198 LINEAR REGRESSION AND CORRELATION Ch. 7 



6. Grades in elementary statistics and in mathematics of finance for the same 

 students are given below. What do you conclude is the relation between a 

 student's grades in these two subjects? Give evidence upon which your con- 

 clusion is based. 



X(statistics): 94 83 91 98 80 82 61 81 58 90 85 75 75 70 92 62 

 y (finance): 89 90 91 97 85 87 41 88 60 85 86 83 87 72 97 64 



7. The following are weights of the larvae of honey bees at different ages: 



Set A. Z(days): 12 3 4 5 6 



7 (milligrams): 2.0 4.3 23.1 93.1 148.7 295.5 



Set 5. X(days): 12 3 4 5 6 



y (log milligrams): 0.30 0.63 1.36 1.96 2.17 2.47 



Construct scatter diagrams for each set separately and decide for which, if 

 either, the assumption of a linear relation between X and Y appears to be justi- 

 fied. If either set produces a satisfactorily linear trend, estimate the slope of 

 the best-fitting freehand line and state what information it provides. Should 

 you make some allowance for the fact that you used a freehand line in a posi- 

 tion with which others might disagree? 



8. Make a scatter diagram for the following pairs of observations. Draw in 

 a freehand line which appears to you to be the best-fitting straight trend line, 

 and derive from this line an estimate of the Y which should correspond, on the 

 average, to X = 0, 4.5, and 7.5 : 



7.2 A METHOD FOR DETERMINING LINEAR 

 REGRESSION (OR TREND) LINES 



It is quite customary to use the term regression line to describe 

 the line chosen to represent the relationship between two variables 

 when this decision is based on sample points, as in a scatter diagram. 

 The origin of the term regression probably lies in genetic studies of 

 the tendency for offspring of parents who are well above, or below, 

 the group average to go back, or "regress," toward that group aver- 

 age. The term trend line will be used interchangeably with regres- 

 sion line, even though the former is frequently associated with dis- 

 cussions of time series. 



Previously, in this chapter, freehand lines have been used to depict 

 the average change of one variable with respect to another. Such 



