关于调查响应与客户支出相关性分析的三类技术疑问

Hey there, let’s break down your three questions clearly based on your market research analysis scenario:

1. Is treating the scaled 1-10 rating as a continuous variable reasonable? #

Short answer: Yes, it’s generally reasonable here, and your approach makes sense given the context.

Your original data is a 0-100 continuous perception scale—you’ve just grouped it into 10 equal bins mapped to 1-10. The key assumption here is that the interval between each scaled score is roughly equivalent (e.g., the difference in perceived service coverage between a 1 and 2 is similar to the difference between a 9 and 10). Since your original scale is a continuous 0-100 measure, this equal-interval assumption holds pretty well.

If you want to validate this, you can run a quick robustness check: compare the results of your linear regression (treating 1-10 as continuous) against an ordered logistic regression (treating it as categorical/ordinal). If the direction and significance of the relationship are nearly identical, you can be confident the continuous variable assumption is safe. With your 4000-sample size, even minor deviations from perfect continuity won’t throw off your results too much.

2. Do I need to normalize the data? What happens if I don’t? #

Short answer: You don’t need to normalize for this univariate linear regression, and skipping normalization is better for your business stakeholders.

Normalization (like min-max scaling) is mostly useful for algorithms that rely on gradient descent (e.g., neural networks) or when you’re comparing coefficients across variables with wildly different scales in a multivariate model. For simple OLS linear regression (your use case), normalization has no impact on the model’s statistical significance or the direction of the relationship—it only changes the scale of the coefficient.

• If you skip normalization: Your regression coefficient will have a direct, business-friendly interpretation: "For every 1-point increase in the scaled perception score, average customer spend increases by $X". This is exactly what your team needs to understand the real-world impact of better perceived service coverage.
• If you normalize: The coefficient loses that dollar-value interpretability. For example, a min-max normalized score (0 to 1) would give you a coefficient like "A full 10-point increase in perception score (from 1 to 10) correlates with a $Y increase in spend"—which is less intuitive for stakeholders who want to know the impact of incremental score changes.

Skipping normalization has no downsides here—your model will run just fine, and the results will be far more actionable.

3. Is normalization appropriate in this specific scenario? #

Short answer: No, it’s not appropriate given your core goal of communicating spend impacts in dollar terms.

Your analysis is focused on a practical business question: "Do customers who rate service coverage higher spend more, and by how much?" Normalization would muddy that clarity by transforming your variables into abstract, unitless scales. Since you’re only running a univariate regression (no other variables to compete with scale), there’s no technical need for normalization either.

The only time normalization might make sense here is if you later expand to a multivariate model with variables on drastically different scales (e.g., adding customer tenure in years alongside spend in dollars). But for your current task, stick with the original scaled score and spend values to keep results interpretable.

内容的提问来源于stack exchange，提问作者user3674232