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

Question

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

BlackTom AI · Accepted Answer

In this question, we are considering the use of the independent variable x to predict the dependent variable y, and we must determine which statement is true.
Since there is only one answer option provided, we will analyze that statement carefully.
Option presented: 'A residual plot graphs residuals against x (or fitted values).' This statement describes a standard diagnostic practice in regression analysis: plotting residuals (the differences between observed y and predicted y) versus the predictor x (or versus the fitted values from the model). Such a plot helps assess several assumptions, including linearity, homoscedasticity (constant variance of residuals), and the presence of potential nonlinear patterns. If residuals display no clear pattern and have roughly constant spread around zero, this supports the adequacy of the linear model and the use of x as a predictor.
If there were additional options, we would evaluate each in terms of how well they align with regression diagnostics. For example, misstatements might claim that residual plots are irrelevant for model checking, or that residuals should be plotted against y or against time in all cases, which would be incorrect customs depending on the model context. However, given the single option provided, the statement about residual plots against x (or fitted values) correctly reflects a primary diagnostic tool in evaluating a model that uses x to predict y.
In summary, the stated option aligns with standard regression diagnostics by advocating residual plots against the predictor or fitted values to check model assumptions and potential inadequacies.

DATA1001/1901 (ND) Revision Quiz 5

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

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