Summary: Arms

Read the summary and the most important questions on ARMS

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• What is the least squares method?

  A method of where we square the errors, so they will always be positive and don't cancel each other. This way we can look for the line that will result in the smallest possible sum of squared errors. 
  We can find a linear regression model which fits the data best.

• What can we check with the standardized residuals?

  Whether there are outliers in the Y-space. 

• What is the rule of thumb for standardized residuals?

  Values must be between -3.3 and +3.3. Those smaller than -3.3, or greater than +3.3 indicate outliers.

• What is the rule of thumb for an outlier in X-space?

  Values of Mahalanobis distance must be lower than 10 + 2 • (number of Independent Variables). Values higher than this critical value indicate outliers.

• What can be echecked with Cook's Distance?

  Whether there are outliers within the XY-space. 

• What are the 3 consquences of multicollinearity?

  - The regression coefficients (B) are unreliable
  - It limits the magnitude of R (the correlation between Y and Ŷ)
  - The importance of individual independent variables can hardly be determined, if at all.

• How can you determine whether multicollinearity is an issue?

  In the last two columns of the coefficients table. You can use the following rule of thumb:
  - Values for the Tolerance smaller than .2 indicate a potential problem.
  - Values for the Tolerance smaller than .1 indicate a problem.
  The variance inflation factor (VIF) is equal to 1/Tolerance. So for the VIF, values greater than 10 indicate a problem.

• What is the adjusted R square?

  An estimate of the proportion of explained variance in the population. It adjusts the value of R2 on the basis of the sample size (n) and the number of predictors in the model (k). 

• What can be the measurement levels of variables that are involved in moderation?

  - An interaction between two continuous variables
  - An interaction between a categorical and a continuous variable
  - An interaction between two categorical variables.

• The ANCOVA test is an omnibus test. What does that mean?

  Multiple comparisons are made with just one statistical test/p-value, and thus with only once a Type I error probability that will not exceed the intended alpha level