![]() In terms of statistical independence of errors, the residuals should be randomly and symmetrically distributed around zero under all conditions. The points should be symmetrically distributed around the horizontal line with a roughly constant variance. In multiple regression models, non-linearity or non-additivity may be tested by systematic patterns in plots of the residuals versus individual explanatory variables. Violations of linearity or additivity are extremely serious: if a linear model is fitted to data which are non-linearly or non-additivity related, then the predictions are likely to be in serious error. Linearity and additivity of the relationship between the dependent and independent variables.There are four principal assumptions supporting the use of linear regression models for purposes of inference: Assumption Testing of Linear Regression Models This is because the goal is to determine which variables are statistically significant and how they relate to changes in the response variable, meaning that the adjusted R‑squared value becomes less important. However, in prediction models used in psychology, the R‑squared values tend to be lower. The results in the report are generally lower than 0.2, which would traditionally be seen as low in many objective prediction models. The values of adjusted R-squared range from 0 to 1, with a value of 1 indicating that the regression line perfectly fits the data. The adjusted R-squared value measures the proportion of the variation in the dependent variable accounted for by the explanatory variables. The ‘goodness of fit’ of a multiple linear regression model can be assessed by considering the adjusted R-squared value produced in the analytical output. Without weighting all the observations are treated equally, which is the preferred option for this report. Weighting allows certain observations to be assigned more weight in the regression analysis (thereby having more influence on the calculated parameter estimates) because it is believed that they are more accurate. Normally in regression analysis it is assumed that the standard deviation of the error term is constant over all values of the explanatory variables. Unlike other results in the report, the multiple linear regression analysis (and logistic regression provided in the accompanying CSV files) is not weighted. Multiple linear regression considers more than one explanatory variable at a time (x 1, x 2, x 3…) and quantifies the strength of relationships between them (recorded as parameter estimates) and the dependent variable y. Linear regression analysis attempts to model the relationship between a dependent variable y (in the case of this report, the ‘motivation index’) and an independent (explanatory) variable denoted x (such as average weekly hours or NHS/HS share).
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