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MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 46: Studentized Residual, Linear Regression, Thoth

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rosi10agarwal
6 Apr 2023
School
Indian Institute of Technology - IIT Kanpur
Department
Mathematics
Course
MTH-416, REGRESSION ANALYSIS
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Document Summary

A residual plot closely related to the partial regression plot in the partial residual plot. It is designed to show the relationship between the study and explanatory variables. X the partial residuals for jx are defined as. When j j i e i x ij. The interpretation of the partial residual plot is very similar to that of the partial regression plot. We may apply certain statistical tests to the residuals to obtain a quantitative measure of some of the model inadequacies. In many applications, residual plots are more informative than the corresponding tests. However, some residual plots do require some skill and experience to interpret. In such cases, the statistical tests may prove useful. The press residuals are defined as where observed study variable based on a model fit to the remaining e i ( ) iy is the predicted value of the. 1,2,, y thi y i n i i.

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Related Questions

which residual plot shows that the line of best fit is a good model?

The Times-Observer is a daily newspaper in Metro City. Like manycity newspapers, the Times-Observer is suffering through difficultfinancial times.The circulationmanager is studying other papers in similar cities in the UnitedStates and Canada. She is particularly interested in what variablesrelate tothe numberof subscriptions to the paper. She is able to obtain the followingsample information on 25 newspapers in similar cities. Thefollowing notationis used:

Sub= Number of subscriptions (in thousands).

Popul = The metropolitan population (in thousands).
Adv= The advertising budget of the paper (in $ hundreds).
Income= The median family income in the metropolitan area (in $thousands).


Paper Sub Popu Adv Income
1 37,95 588,9 13,2 35,1
2 37,66 585,3 13,2 34,7
3 37,55 566,3 19,8 34,8
4 38,78 642,9 17,6 35,1
5 37,67 624,2 17,6 34,6
6 38,23 603,9 15,4 34,8
7 36,9 571,9 11 34,7
8 38,28 584,3 28,6 35,3
9 38,95 605 28,6 35,1
10 39,27 676,3 17,6 35,6
11 38,3 587,4 17,6 34,9
12 38,84 576,4 22 35,4
13 38,14 570,8 17,6 35
14 38,39 586,5 15,4 35,5
15 37,29 544 11 34,9
16 39,15 611,1 24,2 35
17 38,29 643,3 17,6 35,3
18 38,09 635,6 19,8 34,8
19 37,83 598,9 15,4 35,1
20 39,37 657 22 35,3
21 37,81 595,2 15,4 35,1
22 37,42 520 19,8 35,1
23 38,83 629,6 22 35,3
24 38,33 680 24,2 34,7
25 40,24 651,2 33 35,8



(a) Determine the regression equation.

(b) Conduct a global test of hypothesis to determine whether anyof the net regression coefficients are not equal to zero.

(c) Conduct a test for the individual coefficients. Would youconsider deleting any coefficients?

(d) Determine the residuals and plot them against the fittedvalues. Do you see any problems?

(e) Develop a histogram of the residuals. Do you see anyproblems with the normality assumption?

Statistics andProbability

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