Larger values of R2 imply that the observations are more closely grouped about the

Question

BlackTom AI · Accepted Answer

When evaluating what larger R^2 values imply in a simple linear regression context, we want to consider what R^2 represents and how it relates to the data fit.
Option 1: 'average value of the independent variables' — This is not what R^2 measures. R^2 does not describe where the x-values cluster around; it concerns how well the regression model accounts for variability in the dependent variable. So this choice misidentifies the role of the independent variable averages.
Option 2: 'average value of the dependent variables' — Again, R^2 is not about the central tendency (mean) of the y-values. It concerns the proportion of variance explained by the model, not the mean of y. This option confuses variance explained with a simple mean.
Option 3: 'none of the other statements are correct' — This would be a tempting catch-all, but one of the statements does align with a standard interpretation of R^2, so this cannot be true if we accept conventional definitions.
Option 4: 'least squares line' — R^2 measures how well the data points fit the regression line produced by least squares. Higher R^2 means observations are closer to the fitted line, i.e., the model explains more of the variability around the line of best fit. This description matches the core idea of R^2 as the proportion of variance explained by the regression line, indicating tighter clustering around that line.
In summary, the essence of a higher R^2 is that the data align more closely with the regression relationship, which is captured by the least squares line, rather than being tied to averages of x or y alone.

Larger values of R2 imply that the observations are more closely grouped about the

View Explanation

Log in for full answers

Similar Questions

Question at position 11 The coefficient of determination ………….. (Select all that apply)is used to evaluate the goodness of fitis equal to zero for a perfect fittakes values between –1 to +1is equal to negative one for the poorest fit

Calculate R^2 of the regression line for predicting height from shoulder girth, and interpret it in the context of the application.

The correlation coefficient for number of cans of beer and BAC is 0.89. Calculate R^2 and interpret it in context.

In a predictive regression model, in-sample R-squared is computed based on

R-Square question : What is R2 we define total sum of squares (TSS) the explained sum of squares (ESS) the residual sum of squares (RSS)

What is R2 with notations SSR = Sum of Squares REGRESSION SSE = Sum of Squares ERRORS SST = Sum of Squares TOTAL

The closer that the value of R2 is to 1, we would expect:

More Practical Tools for International Students

Homework AI Solver

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler