Final answer:
The coefficient of determination (r²) reflects the proportion of variance in the dependent variable predictable from the independent variables and lies between 0 and 1. The adjusted coefficient can decrease with more predictors if they do not help in explaining variability. Both measures reflect the strength of correlation.
Step-by-step explanation:
The question is about the coefficient of determination (r²) and the adjusted coefficient of determination in the context of statistical analysis of data. The coefficient of determination is a measure that reflects the proportion of variance in the dependent variable which is predictable from the independent variables. It is calculated by squaring the correlation coefficient (r). Therefore, the coefficient of determination is always a positive number between 0 and 1, where a value closer to 1 indicates a stronger linear relationship between the variables.
The adjusted coefficient of correlation accounts for the number of predictors in the model and adjusts the coefficient of determination accordingly. Unlike the regular coefficient of determination, the adjusted version may decrease when more predictors are added to the model if those predictors do not contribute to explaining the variability of the dependent variable. In this way, the adjusted coefficient of determination can help prevent overfitting when multiple predictors are being used.
Therefore, the correct answer to the question of what is true about the coefficient of determination and the adjusted coefficient of correlation is that they reflect the strength of correlation (D). Additionally, the adjusted coefficient of correlation can decrease with more predictors, not because of the increase in predictor numbers per se, but because additional predictors may not be significant. The coefficient of determination and the adjusted coefficient are not always equal and do not necessarily increase with more predictors.