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Chapter 12: Q121E (page 802)

Consider fitting the multiple regression model

Ey=β0+β1x1+β2x2+β3x3+β4x4+β5x5

A matrix of correlations for all pairs of independent variables is given below. Do you detect a multicollinearity problem? Explain.


Short Answer

Expert verified

In this question, x4 and x2 has a correlation of 0.93 and x4 and x5 has a correlation of 0.86. These correlation numbers are very high indicating a strong positive relationship between x4 and x2 and x4 and x5 respectively. Thus, the problem of multicollinearity exists in the model.

Step by step solution

01

Multicollinearity check

Multicollinearity is checked by checking the correlation amongst the independent variables. If there is high correlation amongst any two independent variables, it is said that the problem of multicollinearity exists in the model

02

Application of multicollinearity check

In this question, x4 and x2 has a correlation of 0.93 and x4 and x5 has a correlation of 0.86. These correlation numbers are very high indicating a strong positive relationship between x4 and x2 and x4 and x5 respectively. Thus, the problem of multicollinearity exists in the model.

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Most popular questions from this chapter

Question: Write a first-order model relating to

  1. Two quantitative independent variables.
  2. Four quantitative independent variables.
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Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 12.10 (p. 723). The researchers modelled a movie’s opening weekend box office revenue (y) as a function of tweet rate (x1 ) and ratio of positive to negative tweets (x2) using a first-order model.

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Question: Failure times of silicon wafer microchips. Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer-Level Packaging Conference, November 3–4, 2005). The failure times of the microchips (in hours) were determined at different solder temperatures (degrees Celsius). The data for one experiment are given in the table. The researchers want to predict failure time (y) based on solder temperature (x).

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