Example 8. Weighted Least Squares: Supervisor Data

In a study of industrial establishments of varying size, the number of supervised workers (X) and the number of supervisors (Y) were recorded.

Source: Chatterjee, S. and Price , B. (1991). Regression Analysis By Example. John Wiley & Sons: New York.

Table 8: Supervisor Data

   X     Y
 294    30
 247    32
 267    37
 358    44
 423    47
 311    49
 450    56
 534    62
 438    68
 697    78
 688    80
 630    84
 709    88
 627    97
 615   100
 999   109
1022   114
1015   117
 700   106
 850   128
 980   130
1025   160
1021    97
1200   180
1250   112
1500   210
1650   135

Questions:

1. How adequate is the linear least squares fit? Is any assumption violated?
   
   
2. What is heteroscedasticity? How is it detected? How should one carry out modeling?

Keywords: Weighted Least squares, generalized least squares