The proportion of the variation in the response variable that is explained by the regression model. Show
If there is a perfect linear relationship between the explanatory variable and the response variable there will be some variation in the values of the response variable because of the variation that exists in the values of the explanatory variable. In any real data there will be more variation in the values of the response variable than the variation that would be explained by a perfect linear relationship. The total variation in the values of the response variable can be regarded as being made up of variation explained by the linear regression model and unexplained variation. The coefficient of determination is the proportion of the explained variation relative to the total variation. If the points are close to a straight line then the unexplained variation will be a small proportion of the total variation in the values of the response variable. This means that the closer the coefficient of determination is to 1 the stronger the linear relationship. The coefficient of determination is also used in more advanced forms of regression, and is usually represented by R2. In linear regression, the coefficient of determination, R2, is equal to the square of the correlation coefficient, i.e., R2 = r2. Example The actual weights and self-perceived ideal weights of a random sample of 40 female students enrolled in an introductory Statistics course at the University of Auckland are displayed on the
scatter plot below. A regression line has been drawn. The equation of the regression line is  The coefficient of determination, R2 = 0.822 This means that 82.2% of the variation in the ideal weights is explained by the regression model (i.e., by the equation of the regression line). Curriculum achievement objectives reference Recommended textbook solutions
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63.The ____________________ is the proportion of the total variation in the dependent variableexplained by the regression model.A.Coefficient of determinationB.Correlation coefficientC.SlopeD.Standard error AACSB: Reflective ThinkingBlooms: KnowledgeBowerman - Chapter 13 #63Difficulty: EasyLearning Objective: 13-06 Calculate and interpret the simple coefficients of determination and correlation.Topic: Coefficient of determination 64.A _______________________ measures the strength of the relationship between a dependent variable(Y) and an independent variable (X). AACSB: Reflective ThinkingBlooms: KnowledgeBowerman - Chapter 13 #64Difficulty: EasyLearning Objective: 13-06 Calculate and interpret the simple coefficients of determination and correlation.Topic: Correlation65.r2= .6744sb= .2934For each unit change in X (independent variable), the estimated change in Y (dependent variable) isequal to:The following results were obtained from a simple regression analysis:= 37.2895 - (1.2024)X-1.2024AACSB: AnalyticBlooms: ApplicationBowerman - Chapter 13 #65Difficulty: MediumLearning Objective: 13-01 Explain the simple linear regression model.Topic: Simple Linear Regression66.r2= .6744sb= .2934When X (independent variable) is equal to zero, the estimated value of Y (dependent variable) is equalto: AACSB: AnalyticBlooms: ApplicationBowerman - Chapter 13 #66Difficulty: EasyLearning Objective: 13-01 Explain the simple linear regression model.Topic: Simple Linear Regression67.r2= .6744sb= .2934______________ is the proportion of the variation explained by the simple linear regressionmodel. AACSB: AnalyticBlooms: ApplicationBowerman - Chapter 13 #67Difficulty: EasyLearning Objective: 13-06 Calculate and interpret the simple coefficients of determination and correlation.Topic: Coefficient of determination Newly uploaded documentsWhat is the proportion of variance that can be explained by the regression model?In simple regression, the proportion of variance explained is equal to r2; in multiple regression, it is equal to R2. where N is the total number of observations and p is the number of predictor variables.
Is the percent of variation in the dependent variable that is explained by the regression equation?The coefficient of determination is denoted as r2 , which can be obtained by squaring the correlation coefficient. By definition, the coefficient of determination is the percentage of the variance in the dependent variable that can be described by the independent variables (or regression equation).
What shows the proportion of the total variance that is explained by the independent variable?The simplest way to measure the proportion of variance explained in an analysis of variance is to divide the sum of squares between groups by the sum of squares total. This ratio represents the proportion of variance explained. It is called eta squared or η².
What percentage of the variation in the dependent model is explained by variation in the independent variable?in the values of the dependent variable that can be explained by the variation in the independent variable. R2-value varies from 0 to 1. variance in y can be explained by the changes in X. The remaining 23.46% of the variation in y is presumed to be due to random variability.
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Is the proportion of the total variation in the dependent variable explained by the regression model?
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