If we are using the independent variable to predict the dependent variable , then which of the following statements is true?

Question

If we are using the independent variable  to predict the dependent variable , then which of the following statements is true?

BlackTom AI · Accepted Answer

The provided data for this item lacks the set of answer options, so there is no basis to compare multiple statements. What is given as the proposed answer is: 'A residual plot graphs residuals against x (or fitted values).'

In the context of using an independent variable to predict a dependent variable, a residual plot is a standard diagnostic tool. Plotting residuals (the differences between observed and predicted values) against the independent variable x (or against fitted values) helps to detect potential problems with the model, such as nonlinearity, heteroscedasticity, or unusual patterns indicating model misspecification. If residuals display a random scatter around zero with constant spread, that supports a correctly specified linear relationship.

Why this statement is typically considered true:
- It directly ties residual behavior to the adequacy of using x to predict the response, which is the core concern when assessing a predictive relationship.
- It provides a visual diagnostic that is sensitive to nonlinearity and changing variance, both of which would suggest the model may not be appropriate for the data.
- Plotting residuals against fitted values is another common variant that serves the same diagnostic purpose, helping to reveal patterns tied to the predicted scale.

Why the other potential statements (not shown) might be incorrect, in general terms:
- If an option claimed that residuals should be plotted against the dependent variable, that would be unconventional and unlikely to reveal model issues related to the predictor; residuals are differences and are typically examined against predictors or fitted values.
- An option asserting that residuals should systematically increase or decrease with x to indicate a good fit would be incorrect; a well-fitting linear model tends to show no systematic pattern in residuals.
- Any statement limiting residual analysis to only qualitative judgments, or suggesting residual analysis is unnecessary when using an independent variable, would contradict standard regression diagnostics.

Since the actual list of answer choices is missing, this reasoning focuses on why the stated option about residual plots is a valid diagnostic statement in the context of predicting with an independent variable.

DATA1001 (ND) Evaluate Quiz 5

If we are using the independent variable to predict the dependent variable , then which of the following statements is true?

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