๐ŸŽฌ
Escape Room ยท Residuals & Residual Plots
Director's Cut
A cinema screening room ยท Riviera Studios ยท 11:04 PM
โ† Notes
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๐Ÿ“ Scene Setup You're Josh, an independent data consultant. It's 11pm and you're in Riviera Studios' screening room, laptop open, surrounded by cold coffee cups. At 9am tomorrow, Riviera will sign a $50 million streaming deal based on their analyst's claim that their linear model perfectly predicts IMDb scores from marketing budget.

Your job: verify the residuals before morning. The contract clause is simple, if the model isn't appropriate, the deal doesn't go through. You have 6 pages of the analytics report to sign off on.

๐Ÿ“Š Riviera Studios Dataset, Budget vs IMDb Score

Film Budget (x, $M) Actual IMDb Score (y)
155.8
2105.8
3157.4
4207.7
5258.3
Riviera's Model: ลท = 0.2x + 4
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Page 1 of 6, Verify the Prediction
Using Riviera's model ลท = 0.2x + 4, calculate the predicted IMDb score for Film 3 (budget = $15M).
The analyst's report says 7.0. Do the maths and confirm.
โœ… Page 1 signed off. The prediction checks out, Film 3's predicted score is 7.0.
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Page 2 of 6, First Residual
Film 3 has an actual IMDb score of 7.4. The model predicted 7.0. Calculate the residual for Film 3.
Residual = actual โˆ’ predicted. A positive result means the model under-predicted.
โœ… Page 2 signed off. Residual = +0.4. Film 3's actual score beat the prediction.
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Page 3 of 6, Negative Residual Alert
Film 2 has an actual score of 5.8. The model predicts ลท = 0.2(10) + 4 = 6.0. Calculate the residual for Film 2.
Watch the sign, if the actual value is LESS than the predicted value, the residual is negative. Enter a negative number if needed.
โœ… Page 3 signed off. Residual = โˆ’0.2. The model over-predicted Film 2 by 0.2 points.
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Page 4 of 6, Spot the Outlier
Here are all 5 residuals:
Film 1: +0.8  |  Film 2: โˆ’0.2  |  Film 3: +0.4  |  Film 4: โˆ’0.3  |  Film 5: โˆ’0.7

Which film number has the largest absolute residual? (i.e., the point furthest from the regression line, regardless of sign)
Compare the absolute values: |+0.8| = 0.8, |โˆ’0.2| = 0.2, etc. Enter the film number only.
โœ… Page 4 signed off. Film 1 is the outlier, its residual of 0.8 is the largest. Worth flagging in the report.
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Page 5 of 6, Positive Residuals
Residuals: Film 1: +0.8  |  Film 2: โˆ’0.2  |  Film 3: +0.4  |  Film 4: โˆ’0.3  |  Film 5: โˆ’0.7

How many of the 5 films have a positive residual? (i.e., the actual score was higher than predicted)
Count only the ones with a + sign in front.
โœ… Page 5 signed off. 2 films have positive residuals (Films 1 and 3). Now for the final judgement call...
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Page 6 of 6, The Final Verdict
You check the residual plots for two studios competing for the deal:

Studio A (Riviera): Residual plot shows points scattered randomly above and below zero, no discernible pattern, small residuals throughout.

Studio B (rival): Residual plot shows a clear U-shaped curve, residuals are strongly positive at low x values, negative in the middle, and positive again at high x values.

Which studio's model is appropriate for linear regression? Enter 1 for Studio A or 2 for Studio B.
Remember: random scatter = linear model is appropriate. A clear pattern = non-linear relationship, linear model is NOT appropriate.
โœ… Page 6 signed off. Studio A (Riviera) shows random scatter, linear model appropriate!
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Director's Cut: Complete
You've signed off on all 6 pages. Riviera's residual plot shows random scatter, the linear model IS appropriate. The contract stands. The $50M deal goes through.

Film 1 was flagged as an outlier (residual 0.8), but the overall model fits the data well. Studio B's U-shaped residual plot? That model's going straight to the cutting room floor. ๐Ÿ—‘๏ธ
residual = actual โˆ’ predicted  ยท  random scatter โ†’ linear model appropriate  ยท  pattern โ†’ non-linear model needed
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