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Analysis and Reporting of Field Study Data
Published in Fergus Nicol, Michael Humphreys, Susan Roaf, Adaptive Thermal Comfort, 2012
Fergus Nicol, Michael Humphreys, Susan Roaf
Regression analysis can be extended to include more than one environmental variable by the use of multiple correlation and regression. In this way a new ‘index’ of thermal comfort can be constructed, as was done by Bedford (1936), Sharma and Ali (1986) and a number of other workers since. In multiple linear regression the resulting equation will have the form C=a+bE1+cE2+…
Results of the Statistical Analysis of the Cases
Published in Floris van den Broek, Management of International Networks, 1999
The correlation expresses the strength and the nature of the relationship between the independent and the dependent variables. Falling between −1 and +1, it shows a strong relationship when it is a high absolute number. Thus, a correlation of 0 shows no linear association between the input and the output. The negative sign indicates that when the independent variable increases, the dependent variable decreases or vice versa. The positive sign signals that the independent and the dependent variables move in the same direction. In the case of multiple regressions, the multiple correlation explains the overall strength of the relationship between all the independent variables and the dependent variable.
Multivariate Methods
Published in Shayne C. Gad, Carrol S. Weil, Statistics and Experimental Design for Toxicologists, 1988
(with X’s being independent of predictor variables and Y’s being dependent variables or outcome measures). One of the outputs from the process will be the coefficient of multiple correlation, which is simply the multivariate equivalent of the correlation coefficient (r).
Probabilistic Model for Shear Strength of RC Interior Beam Column Joints
Published in Journal of Earthquake Engineering, 2021
Vandana R K, Bindhu KR, Baiju KV
The IBM SPSS 21 [2013] software package was engaged to obtain the multiple linear regression coefficients. The strength of the relationship between the independent variables and the dependent variable is designated with R and is usually referred to as the multiple correlation coefficients. This square of this number (R2) yields a value that represents the proportion of variation in the response variable that is explained by the predictor variables. The adjusted R2 is a modified version of R2 that has been adjusted for the number of predictors in the model. The adjusted R2 increases only if the new term improves the model more than expected. It decreases when a predictor improves the model by less than expected. The p-value in the multiple linear regression for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low value (p < 0.05) indicates that the null hypothesis can be rejected. That is, a predictor with a low p-value is likely to be a meaningful addition to the model because changes in the predictor’s value are related to those in the response variable. The standard error of estimate is another goodness-of-fit statistic to indicate the accuracy of predictions. It provides an overall measure of how well the model fits the data. This statistic explains the average inaccuracy level of the regression model by using the units of the dependent variable. Smaller values are more favorable because they indicate that the predictions are closer to the actual values [Draper and Smith, 1998; Hosmer et al., 2013].