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In: Statistics and Probability

What are multiple linear egression analysis several key assumptions? Please list them and then choose one...

What are multiple linear egression analysis several key assumptions? Please list them and then choose one and explain it in detail. Make sure that you choose one that has not been selected before

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Expert Solution

Multiple linear regression analysis makes several key assumptions are as follows -

  • There must be a linear relationship between the result variable and the independent variables. Scatter charts can show if there is a linear or curvilinear relationship.
  • Multivariate normality: multiple regression assumes that residues are normally distributed.
  • No multicollinearity: multiple regression assumes that independent variables are not highly correlated with each other. This hypothesis is tested using the Variance Inflation Factor (VIF) values.
  • Homoscedasticity: this hypothesis states that the variance of the error terms is similar between the values of the independent variables. A plot of residuals standardized with respect to the expected values can show if the points are equally distributed over all the values of the independent variables.Intellectus statistics automatically include intake tests and diagrams when a regression is performed.

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EXPLANATION

Multiple linear regression requires at least two independent variables, which can be nominal, ordinal, or interval/ratio variables. An empirical rule for sample size is that regression analysis requires at least 20 cases per independent variable in the analysis.

  1. First of all, multiple linear regression requires that the relationship between independent and dependent variables is linear. The linearity hypothesis can be better tested with scatterplots.
  2. Secondly, multiple linear regression analysis requires that errors between observed and expected values (ie, regression residuals) should normally be distributed. This hypothesis can be verified by observing a histogram or a Q-Q-Plot. The normality can also be verified with a test of goodness of adaptation (for example, the Kolmogorov-Smirnov test), although this test should be conducted on the residues themselves.
  3. Third, multiple linear regression assumes that there is no multicollinearity in the data. Multicollinearity occurs when independent variables are too closely related to each other. Multicollinearity can be controlled in different ways:
  • Correlation matrix - When calculating an array of Pearson bivariate correlations among all the independent variables, the extent of correlation coefficients should be less than 0.80.
  • Variance Influence Factor (VIF) - Linear Regression VIFs indicate the degree to which variances in regression estimates have increased due to multicollinearity. VIF values above 10 indicate that multicollinearity is a problem.
  • If multicollinearity is found in the data, a possible solution is to center the data. To center the data, subtract the average score from each observation for each independent variable. However, the simplest solution is to identify the variables that cause multicollinearity problems (ie, through correlations or VIF values) and by removing these variables from the regression.
  1. 4. The last hypothesis of multiple linear regression is homoscedasticity. A dispersion plot of residues with respect to expected values is a good way to verify homoscedasticity. There should be no clear patterns in the distribution; if there is a cone-shaped model, the data are heteroscedastic.If the data is heteroscedastic, a non-linear data transformation or the addition of a quadratic term could solve the problem.

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