Based on the output of summary() for the model from the previous question, interpret the interaction between nox and dis in the context of predicting medv. Choose the correct interpretation:

Question

Based on the output of summary() for the model from the previous question, interpret the interaction between nox and dis in the context of predicting medv. Choose the correct interpretation:

BlackTom AI · Accepted Answer

The prompt asks us to interpret the interaction between nox and dis from the summary() output for predicting medv. Since there is only one provided answer option, we will examine why this single interpretation is consistent and what it implies, while also noting the absence of alternative choices to contrast.
First, consider what an interaction term between nox and dis would mean in a regression predicting medv. An interaction implies that the effect of dis on medv changes depending on the level of nox. In other words, the slope of dis with respect to medv is not constant across all values of nox; instead, it varies with nox.
The given interpretation states: 'The effect of dis on medv changes depending on the value of nox, with an interaction term of approximately -8.95, indicating a stronger negative impact of dis on medv when nox is higher.' This aligns with standard interpretation of a negative interaction coefficient: as nox increases, the marginal effect of dis on medv becomes more negative (i.e., higher nox amplifies the negative association between dis and medv).
Next, assess what the numerical value of the interaction term (approximately -8.95) conveys. A negative coefficient around -8.95 suggests that for each unit increase in nox, the effect of dis on medv decreases by about 8.95 units of medv, assuming all other predictors are held constant. Practically, this means at higher nox levels, dis is associated with more substantial reductions in medv, relative to lower nox levels. The magnitude statement—'stronger negative impact of dis on medv when nox is higher'—captures this directional and conditional relationship, provided the scale of variables supports such interpretation and there are no multicollinearity or model specification issues.
Now, given there are no alternative options provided in answer_choices, we cannot evaluate other potential interpretations or common pitfalls. In a typical scenario, other tempting but incorrect options might claim there is no interaction, or that the interaction flips the direction of dis's effect, or misattribute the meaning of a negative interaction term. Understanding why those would be incorrect helps reinforce the correct interpretation:
- Claiming no interaction exists would be inconsistent with a reported interaction term; the model explicitly includes an interaction between dis and nox, so the effect of dis depends on nox by design.
- Stating that the interaction changes the overall sign of dis’s effect in all contexts would be an overreach; the sign of the marginal effect of dis depends on the level of nox, not that dis becomes universally negative or positive in all cases.
- Misinterpreting the coefficient as the main effect of dis ignores the fact that the interaction term modifies dis’s effect across values of nox rather than representing dis’s isolated impact.
- Assuming the exact numeric interpretation (e.g., the precise units or scaling) without knowing the data scale, centering, or which variables were standardized would be speculative; the qualitative takeaway remains the conditional change in dis’s effect with nox, while the exact numeric magnitude should be interpreted in the context of the data preprocessing.
In summary, the provided interpretation correctly identifies that there is an interaction where dis’s effect on medv depends on nox, and that the negative interaction coefficient points to a stronger negative association between dis and medv at higher nox levels. The absence of alternative answer options means we cannot contrast this with other potential interpretations within this item, but the described reasoning faithfully reflects standard interaction interpretation in a regression framework.

SDS 324E Homework 10

Based on the output of summary() for the model from the previous question, interpret the interaction between nox and dis in the context of predicting medv. Choose the correct interpretation:

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