194 LINEAR REGRESSION AND CORRELATION Ch. 7 



The trend line drawn into Figure 7.015 was determined just "by 

 eye"; but it usually is preferable to have a standard method of de- 

 termining where the line should be drawn. This matter will be dis- 

 cussed in the following four sections. 



7.1 SCATTER DIAGRAMS AND TYPES OF TREND LINES 



A number of the statistical methods with which the reader is al- 

 ready familiar can be employed in the analysis of data involving two 

 variables. One additional matter must be studied, however, namely, 

 the relationship between the two variables. A little graphic analysis 

 usually is worth while before the numerical analyses are undertaken. 



There are many ways in which one variable, Y, can change with 

 respect to another variable, X, as successive pairs of observations 

 are taken with the X, say, increasing in magnitude. The size of Y 

 may tend to increase as X increases; Y may tend to decrease as X 

 increases; or some of both may occur over the range of values studied. 

 In addition there are numerous ways in which Y can increase as X 

 increases; and similarly for the other possibilities just mentioned. 

 To illustrate, consider the following tables of pairs of values for X 

 and Y: 



It is helpful to a mathematical study of the relationship between 

 two variables if the pairs of corresponding numerical measurements, 

 X and Y, are represented by points on a graph, as they were in ele- 

 mentary algebra. This has been done in Figures 7.114, B, . . . , G 

 for the data immediately above. 



Such graphs are called scatter diagrams. It is noted from these 

 figures that the points may not exactly fit any simple curve, but they 

 sometimes do exhibit a general pattern which may make it possible to 

 study the relationship between Y and X. It is necessary here to 



