Which index evaluates how well a model fits the data used to generate it?

Which index evaluates how well a model fits the data used to generate it?

• A. Goodness of fit
• B. P-value
• C. Confidence interval
• D. Effect size

Answer: (A)

The main idea here is goodness of fit—the metric that describes how closely a model reproduces the data it was built from. When we fit a model, we’re adjusting parameters to minimize the differences between observed values and predicted values. A goodness-of-fit index summarizes how well those predictions match the actual data, using the same dataset that produced the model. Examples include chi-square goodness-of-fit tests for categorical data and R-squared or related residual-based measures in regression, which express how much of the observed variation the model accounts for. The other options don’t serve this purpose. A p-value tells us how surprising the observed data would be if a null hypothesis were true, not how well the model fits the data. A confidence interval gives a range for a parameter estimate with a certain level of certainty, not a fit assessment. An effect size measures the magnitude of an observed effect, again not the model’s fit to the data. So the index that directly evaluates how well the model matches the data used to generate it is goodness of fit.

The main idea here is goodness of fit—the metric that describes how closely a model reproduces the data it was built from. When we fit a model, we’re adjusting parameters to minimize the differences between observed values and predicted values. A goodness-of-fit index summarizes how well those predictions match the actual data, using the same dataset that produced the model. Examples include chi-square goodness-of-fit tests for categorical data and R-squared or related residual-based measures in regression, which express how much of the observed variation the model accounts for.

The other options don’t serve this purpose. A p-value tells us how surprising the observed data would be if a null hypothesis were true, not how well the model fits the data. A confidence interval gives a range for a parameter estimate with a certain level of certainty, not a fit assessment. An effect size measures the magnitude of an observed effect, again not the model’s fit to the data. So the index that directly evaluates how well the model matches the data used to generate it is goodness of fit.