Final answer:
The statement that 'the standard error of the estimate can take on negative values' is false because the standard error is always zero or positive, reflecting the variability in the data and it measures the accuracy of the regression model without a predefined upper limit. Therefore correct option is B
Step-by-step explanation:
The student question is asking which of the following statements about the standard error of the estimate is not true. To answer this, we need to understand the concept of standard error in statistical analysis.
Firstly, the standard error of the estimate is indeed based on the squared deviations between the actual and predicted values of the response variable. This is known as the sum of squares of the residuals and is used to measure the total error of the regression model.
Secondly, a critical characteristic of the standard error, similar to the standard deviation, is that it can never be negative. It is always zero or a positive value, reflecting variability or spread in the data.
Thirdly, the standard error is a gauge for the accuracy of the regression model. A smaller standard error typically indicates that the regression model predicts the response variable more accurately.
Finally, in theory, the standard error of the estimate does not have a predefined upper limit. It will increase as the variability in the data increases.
Given this information, the statement that 'it can take on negative values' is not true of the standard error of the estimate.