Summer is coming to Coastal Bay. The local council needs to plan their lifeguard roster, but they can only afford to staff up when visitor numbers justify it.
They've built a regression model from last season's data: daily maximum temperature vs beach visitors. Six data challenges stand between you and a safe, well-staffed summer beach. 🏖️
PROGRESS0 / 6 complete
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1
Opening the Model
Active
The council's data analyst presents the regression model she built from last season. It predicts daily visitor numbers from the daily maximum temperature.
Equation:Visitors = 20t − 300
t =max temp (°C)
Data range:18°C to 32°C
Use the model to predict visitor numbers on a day with a maximum temperature of 20°C.
Substitute t = 20 into the equation: Visitors = 20(20) − 300.
2
Heatwave Forecast
Locked
The Bureau of Meteorology is predicting a heat wave next week. The council needs an estimate for their busiest day to arrange extra lifeguards.
Equation:Visitors = 20t − 300
Forecast temperature:28°C
Predict the number of visitors expected on the 28°C heat wave day.
Substitute t = 28 into Visitors = 20t − 300.
3
Reading the Slope
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The council's lifeguard coordinator wants to understand exactly how sensitive visitor numbers are to temperature changes. She needs to justify her staffing decisions to the mayor.
Equation:Visitors = 20t − 300
According to the model, how many extra visitors come to the beach for each 1°C increase in maximum temperature?
The slope (gradient) is the number multiplied by t in the equation. It tells you how much y changes for each 1-unit increase in t.
4
Staffing Threshold
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Beach safety regulations require a minimum of one extra lifeguard for every 100 visitors. The council decides to call in the extra team when predicted visitor numbers hit 400.
Equation:Visitors = 20t − 300
Target visitors:400
At what maximum temperature does the model predict visitor numbers will reach 400? Solve for t.
Set 400 = 20t − 300. Add 300 to both sides, then divide both sides by 20.
5
Checking the Record
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The analyst pulls last season's records to check how accurate the model actually was. She finds one day where the actual count was different from the prediction.
Temperature that day:25°C
Model prediction:20(25) − 300 = 200 visitors
Actual visitors:210
Residual =actual − predicted
Calculate the residual for this day. A positive residual means the beach was busier than predicted.
Residual = actual − predicted = 210 − 200 = ?
6
How Good is the Model?
Locked
The mayor asks the analyst one final question before approving the summer safety budget: "How much of the variation in beach visitors is actually explained by temperature?"
Pearson's r:r = 0.95
r² =r × r
Calculate r² (to 2 decimal places). This percentage of variation in visitor numbers is explained by temperature.
r² = 0.95 × 0.95 = ? Round your answer to 2 decimal places (e.g. 0.90).
🏖️🌊
Summer Sorted!
The council has everything they need. Lifeguard roster approved, budget signed, beach safe.
You've worked through prediction, gradient interpretation, solving for x, residuals and r², that's the full regression toolkit. Well done! ☀️