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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.
  3. Five quantitative independent variables.

Suppose you fit the model y =β0+β1x1+β1x22+β3x2+β4x1x2+εto n = 25 data points with the following results:

β^0=1.26,β^1= -2.43,β^2=0.05,β^3=0.62,β^4=1.81sβ^1=1.21,sβ^2=0.16,sβ^3=0.26, sβ^4=1.49SSE=0.41 and R2=0.83

  1. Is there sufficient evidence to conclude that at least one of the parameters b1, b2, b3, or b4 is nonzero? Test using a = .05.

  2. Test H0: β1 = 0 against Ha: β1 < 0. Use α = .05.

  3. Test H0: β2 = 0 against Ha: β2 > 0. Use α = .05.

  4. Test H0: β3 = 0 against Ha: β3 ≠ 0. Use α = .05.

Question:How is the number of degrees of freedom available for estimating σ2(the variance ofε ) related to the number of independent variables in a regression model?


Factors that impact an auditor’s judgment. A study was conducted to determine the effects of linguistic delivery style and client credibility on auditors’ judgments (Advances in Accounting and Behavioural Research, 2004). Two hundred auditors from Big 5 accounting firms were each asked to perform an analytical review of a fictitious client’s financial statement. The researchers gave the auditors different information on the client’s credibility and linguistic delivery style of the client’s explanation. Each auditor then provided an assessment of the likelihood that the client-provided explanation accounted for the fluctuation in the financial statement. The three variables of interest—credibility (x1), linguistic delivery style (x2) , and likelihood (y) —were all measured on a numerical scale. Regression analysis was used to fit the interaction model,y=β0+β1x1+β2x2+β3x1x2+ε . The results are summarized in the table at the bottom of page.

a) Interpret the phrase client credibility and linguistic delivery style interact in the words of the problem.

b) Give the null and alternative hypotheses for testing the overall adequacy of the model.

c) Conduct the test, part b, using the information in the table.

d) Give the null and alternative hypotheses for testing whether client credibility and linguistic delivery style interact.

e) Conduct the test, part d, using the information in the table.

f) The researchers estimated the slope of the likelihood–linguistic delivery style line at a low level of client credibility 1x1 = 222. Obtain this estimate and interpret it in the words of the problem.

g) The researchers also estimated the slope of the likelihood–linguistic delivery style line at a high level of client credibility 1x1 = 462. Obtain this estimate and interpret it in the words of the problem.

Question: The Excel printout below resulted from fitting the following model to n = 15 data points: y=β0+β1x1+β2x2+ε

Where,

x1=(1iflevel20ifnot)x2=(1iflevel30ifnot)

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