![]() ![]() The relationship between the dependent variable and each independent variable should be linear and all observations should be independent. The variance of the distribution of the dependent variable should be constant for all values of the independent variable. But thats exactly what the OLS black box is minimizing when given the data table consisting of the 'weighted' tuples (wi,wixi. ![]() By definition, weighted least squares minimizes. Other assumptions: For each value of the independent variable, the distribution of the dependent variable must be normal. When there are weights, necessarily positive, we can write them as w2i w i 2.Categorical variables, such as religion, major field of study or region of residence, need to be recoded to binary (dummy) variables or other types of contrast variables. Data: Dependent and independent variables should be quantitative.Plots: Consider scatterplots, partial plots, histograms and normal probability plots.Also, consider 95-percent-confidence intervals for each regression coefficient, variance-covariance matrix, variance inflation factor, tolerance, Durbin-Watson test, distance measures (Mahalanobis, Cook and leverage values), DfBeta, DfFit, prediction intervals and case-wise diagnostic information. For each model: Consider regression coefficients, correlation matrix, part and partial correlations, multiple R, R2, adjusted R2, change in R2, standard error of the estimate, analysis-of-variance table, predicted values and residuals.For each variable: Consider the number of valid cases, mean and standard deviation.Assumptions to be considered for success with linear-regression analysis: ![]()
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