Weighted Least Squares A full professor of statistics at a major US university i
ID: 3249455 • Letter: W
Question
Weighted Least Squares A full professor of statistics at a major US university is interested in estimating the third quartile of salaries for full professors with 6 years of experience in that rank. Data, in the form of 2005-2006 Salary Report of Academic Statisticians are available below. Using weighted least squares, estimate the 2005-2006 third quartile for salary of full professors with 6 years experience.
YearsOfExperience Samplesizeni 3rdQuartile 101300 111303 98000 124000 128475 117410 115825 134400 128066 164700 0300505060 00007-2060 e3300448407 1184875484 rt 0 1 9 2 2 1 1 3 2 6 1111111 7395808149 1312165331 0246827284 11223Explanation / Answer
Years of experience as a full professor
Sample size, ni
Third quartile ($)
0
17
101300
2
33
111303
4
19
98000
6
25
124000
8
18
128475
12
60
117410
17
58
115825
22
31
134300
28
34
128066
34
19
164700
Using reciprocal of the “Sample size” as weights, this weighted least squares regression analysis was performed. The output of WLS obtained using R is contained in Figure 1.
The required WLS regression equation is,
Third quartile = 103,925.6 + 1,517.9 Experience
The estimate of the 2005–2006 third quartile for salary of full professors with 6 years of experience is $113,033.
Years of experience as a full professor
Sample size, ni
Third quartile ($)
0
17
101300
2
33
111303
4
19
98000
6
25
124000
8
18
128475
12
60
117410
17
58
115825
22
31
134300
28
34
128066
34
19
164700
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