A statistical measure that determines the proportion of variance in the dependent variable that can be explained by the independent variable Show
What is the Coefficient of Determination?The coefficient of determination (R² or r-squared) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable. In other words, the coefficient of determination tells one how well the data fits the model (the goodness of fit).  Although the coefficient of determination provides some useful insights regarding the regression model, one should not rely solely on the measure in the assessment of a statistical model. It does not disclose information about the causation relationship between the independent and dependent variables, and it does not indicate the correctness of the regression model. Therefore, the user should always draw conclusions about the model by analyzing the coefficient of determination together with other variables in a statistical model. The coefficient of determination can take any values between 0 to 1. In addition, the statistical metric is frequently expressed in percentages. Interpretation of the Coefficient of Determination (R²)The most common interpretation of the coefficient of determination is how well the regression model fits the observed data. For example, a coefficient of determination of 60% shows that 60% of the data fit the regression model. Generally, a higher coefficient indicates a better fit for the model. However, it is not always the case that a high r-squared is good for the regression model. The quality of the coefficient depends on several factors, including the units of measure of the variables, the nature of the variables employed in the model, and the applied data transformation. Thus, sometimes, a high coefficient can indicate issues with the regression model. No universal rule governs how to incorporate the coefficient of determination in the assessment of a model. The context in which the forecast or the experiment is based is extremely important, and in different scenarios, the insights from the statistical metric can vary. Calculation of the CoefficientMathematically, the coefficient of determination can be found using the following formula: Where:
Although the terms “total sum of squares” and “sum of squares due to regression” seem confusing, the variables’ meanings are straightforward. The total sum of squares measures the variation in the observed data (data used in regression modeling). The sum of squares due to regression measures how well the regression model represents the data that were used for modeling. More ResourcesTo keep learning and advancing your career, the additional CFI resources below will be useful:
h琀琀ps://www.coursehero.com/昀椀le/15618819/PCQ03/ h琀琀p://crystalxueyan.blogspot.com/2014/08/bus105-3-second-try.html h琀琀ps://www.coursehero.com/昀椀le/15618819/PCQ03/ Question 15 pts What does the coefficient of correlation indicate? The coefficient of correlation shows the strength of the linear (straight line) relationship between two interval or ratio scale variables. The coefficient of correlation shows the rate of change between two interval or ratio scale variables. The coefficient of correlation shows the direction and strength of the linear (straight line) relationship between two interval or ratio scale variables. The coefficient of correlation shows the direction of the linear (straight line) relationship between two interval or ratio scale variables. Question 25 pts Which of the following statements is NOT a characteristic of Variance Inflation Factor (VIF)? A VIF of greater than 10 is unsatisfactory. Lower VIF is preferred. An independent variable with unsatisfactory VIF should not be removed from the model. VIF is used to assess the degree to which an independent variable is correlated to other independent variables in a multiple regression. Question 35 pts To interpret validly, a correlation coefficient of -0.85 would indicate a_______________________. strong positive correlation weak negative correlation weak positive correlation strong negative correlation Question 45 pts When discussing appropriate multiple regression analysis, which of the following is an assumption of multiple regression? I. The variations in residuals are not the same for small and large values of predicted Y. II. The independent variables are correlated. III. The residuals are independent. What is the variation in the dependent variable that is explained by the variation in the independent variable?Answer and Explanation: Coefficient of determination: It represents the proportion of the variation that can be explained in the dependent variable using the independent variable.
What is the meaning of the coefficient associated with dependent variable?The coefficient value signifies how much the mean of the dependent variable changes given a one-unit shift in the independent variable while holding other variables in the model constant.
Is RBoth are unitless measures that are indicative of model fit, but they define model fit in two different ways: CV evaluates the relative closeness of the predictions to the actual values while R-squared evaluates how much of the variability in the actual values is explained by the model.
What is the difference between R and R2?R: The correlation between the observed values of the response variable and the predicted values of the response variable made by the model. R2: The proportion of the variance in the response variable that can be explained by the predictor variables in the regression model.
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