Key driver analysis
Relative importance analysis
How results are checked
Named statistical review pending. Selected automated reference cases are published on the validation page.Top driver of overall satisfaction
30.6%of R²
Quality, then Service (24.9%)
Shapley decomposition · model R² = 0.705
Relative importance analysis answers “which attributes move overall satisfaction most?” when the attribute ratings are correlated with one another. It splits the model's R² into a share per driver: Shapley value regression averages each driver's added R² over every possible ordering of the drivers, and Johnson's relative weights reach nearly the same split through an eigen-decomposition. Both shares add up to R², unlike standardized betas, which can be near zero or negative for a driver that clearly matters. This tool runs both on your file in the browser, free, with no account, and the file is never uploaded.
Run a key driver analysis online
Open a CSV, Excel, SPSS, Stata, SAS or JSON file (or the synthetic sample), choose the outcome (for example overall satisfaction or likelihood to recommend), tick 2–15 driver ratings and optionally a weight column. Rows missing any selected column are dropped and the base is shown. Results update as you change the selection; bootstrap intervals for the Shapley shares are computed only when you ask for them.
CSV, Excel, SPSS, Stata, SAS, R, Parquet, SQLite or JSON. The file is read in this browser tab and never uploaded.
Why not just use regression betas or correlations?
Survey attribute ratings share a halo: people who like a brand rate it higher on everything. With correlated drivers, standardized betas depend on which other drivers are in the model, can flip sign, and do not add up to anything meaningful. Simple correlations ignore the overlap entirely, so every halo-laden attribute looks important.
Relative importance methods sit between the two. They credit each driver with the variance it explains on its own and a fair share of the variance it explains jointly with others, so the shares are non-negative in practice and sum to R². For a binary outcome (buy / not buy, churn / stay), see the logistic key driver analysis guide.
Reading the quadrant map
The quadrant map plots each driver's importance (Shapley share of R²) against its performance (the mean rating, shown as a position between the lowest and highest observed rating). The dividing lines sit at the average share (100% ÷ number of drivers) and the average performance across drivers. Fix first: important but rated below average. Maintain: important and rated well. Lower priority: less important and rated below average. Possible overkill: rated well on something that explains little of the outcome. The splits are relative to the drivers you entered, so adding or removing a driver moves the lines.
The method
Formula
φⱼ = Σ_{S ⊆ D∖{j}} |S|! (p − |S| − 1)! / p! · [R²(S ∪ {j}) − R²(S)]
where
- D, p
- the set of drivers and its size (2–15 here)
- R²(S)
- R² of the regression of the outcome on the drivers in subset S, computed from the correlation matrix as r_yS′ R_SS⁻¹ r_yS (R²(∅) = 0)
- φⱼ
- driver j's Shapley value; Σⱼ φⱼ = R² of the full model. All 2^p subset models are fitted once and cached
- εⱼ = Σₖ λⱼₖ² βₖ*²
- Johnson's relative weight: with R_xx = VΛV′, the loadings Λ* = VΛ^½V′ link drivers to their closest orthogonal counterparts Z, and β* = Λ*⁻¹ r_xy are the regression weights of the outcome on Z. Σⱼ εⱼ = R²
- % of R²
- φⱼ / R² × 100 (or εⱼ / R² × 100) — the driver's share of the explained variance
Worked example
The synthetic sample has 600 respondents rating six service attributes and overall satisfaction on 1–10 scales. The attributes share a halo, so their correlations with overall satisfaction are all between 0.48 and 0.70.
The full model explains R² = 0.705. Shapley value regression credits sat_quality with 0.216 of that (30.6% of R²) and sat_service with 24.9%; Johnson's relative weights give 30.7% and 24.9%. The full ranking by Shapley share is sat_quality 30.6%, sat_service 24.9%, sat_price 18.4%, sat_speed 9.6%, sat_range 9.2%, sat_website 7.3%.
Compare the standardized betas: sat_website has β = -0.004, which would suggest it is irrelevant, yet it correlates r = 0.48 with the outcome and receives 7.3% of R² once its shared variance is split fairly. On the quadrant map, sat_price falls in Fix first: above-average importance with below-average ratings. The driver means only range from 6.34 to 6.49 here, so the performance split is a close call; on real data, check whether the gaps are large enough to matter.
Using it well
When to use it
Use it when
- Use: Satisfaction, loyalty or brand-equity studies with a numeric outcome and several correlated attribute ratings.
- Use: You need importance shares that add up to the explained variance, for a chart or a priority list.
- Use: Standardized betas look implausible (near zero or negative for a driver that clearly matters).
Not the right tool when
- Avoid: The outcome is binary (bought / did not) — use logistic models; see the key driver analysis guide.
- Avoid: You want to predict the effect of changing a driver — importance shares are associative, not causal.
- Avoid: Fewer than about 10 complete respondents per driver, or drivers that are near-duplicates of each other.
How to interpret it
Rule of thumb
Read the share of R², not the raw number: a driver with 30% of R² explains roughly twice as much of the outcome's explained variance as one with 15%. Shapley and Johnson shares normally agree within a percentage point or two; treat differences smaller than the bootstrap interval width as ties. Importance is associative, not causal.
Questions
Frequently asked questions
What is the difference between Shapley value regression and Johnson's relative weights?
Shapley value regression is exact: it fits the regression for every subset of drivers (2^p models) and averages each driver's incremental R² over all orderings. Johnson's relative weights approximate the same decomposition in one step by regressing the outcome on orthogonal counterparts of the drivers. Both sum to R², and in practice they usually agree within a point or two; with orthogonal drivers both equal the squared correlations.
Why do some drivers have a near-zero or negative beta but a sizeable share?
A beta is the effect of a driver holding all other drivers constant. When drivers overlap, the shared variance is credited to whichever driver the regression happens to favour, and the others can get betas near zero or even negative. Shapley and relative weights divide that shared variance among the drivers instead, so a driver that is strongly related to the outcome keeps a share of the credit.
Does a high importance share mean improving that attribute will raise satisfaction?
No. Importance shares describe how ratings move together in your data. They do not show that changing an attribute would change the outcome; that needs an experiment or a causal design. Use the shares to prioritise what to investigate, not as a forecast.
How are missing values and weights handled?
Rows missing the outcome, any selected driver or the weight (or with a non-positive weight) are dropped, and the base n and dropped count are shown. With a weight column, the means and correlations are weighted, and the decomposition is computed from the weighted correlation matrix.
What do the bootstrap intervals show?
They are 95% percentile intervals for each driver's Shapley share, from up to 200 resamples of the complete rows drawn with a fixed seed, so the same data always gives the same intervals. Overlapping intervals mean the ranking between those drivers is not well determined by this sample.
Sources and next steps
References & further reading
- [1]Johnson, J. W. (2000). A heuristic method for estimating the relative weight of predictor variables in multiple regression. Multivariate Behavioral Research, 35(1), 1–19.
- [2]Lipovetsky, S., & Conklin, M. (2001). Analysis of regression in game theory approach. Applied Stochastic Models in Business and Industry, 17(4), 319–330.
- [3]Grömping, U. (2006). Relative importance for linear regression in R: the package relaimpo. Journal of Statistical Software, 17(1), 1–27.doi.org
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