Artificial Intelligence
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Can you please provide the Chi Squared formula given the helper formulas provided SELECT Bet = COUNT(*) OVER (), Collect = SUM(CASE WHEN Result = 1 THEN ([BetfairWinSP ] - 1) * 0.95 + 1 END) OVER (), Profit = SUM(CASE WHEN Result = 1


To calculate the Chi-Squared statistic using the provided helper calculations, you will need observed frequencies and expected frequencies for the categories of your data. The general formula for the Chi-Squared statistic (\( \chi^2 \)) is: \[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \] Where: - \( O_i \) = Observed frequency for category \( i \). - \( E_i \) = Expected frequency for category \( i \). ### Given your context: Assuming that: - Your observed frequencies can be derived from the results of bets (where `Result = 1` indicates a win and another value indicates a loss). - Expected frequencies could be calculated based on the proportion of wins and losses or based on a theoretical distribution. ### Using SQL to implement Chi-Squared calculation might look like this: Assuming we have two categories (wins and losses) for simplicity: 1. **Calculate Observed Frequencies**: - Wins (from your `Wins` calculation) - Losses (Total bets - Wins) 2. **Calculate Expected Frequencies**: - This could be a uniform distribution based on the total bets or a theoretical proportion based on prior data. ```sql WITH BettingData AS ( SELECT COUNT(*) OVER () AS TotalBets, COUNT(CASE WHEN Result = 1 THEN 1 END) OVER () AS Wins, COUNT(CASE WHEN Result <> 1 THEN 1 END) OVER () AS Losses ) SELECT (POWER(Wins - ExpectedWins, 2) / NULLIF(ExpectedWins, 0)) + (POWER(Losses - ExpectedLosses, 2) / NULLIF(ExpectedLosses, 0)) AS ChiSquared FROM BettingData CROSS JOIN ( SELECT TotalBets / 2.0 AS ExpectedWins, -- e.g., assume equal distribution of wins and losses TotalBets / 2.0 AS ExpectedLosses FROM BettingData ) AS Expected ``` ### Explanation: 1. The `WITH BettingData AS` Common Table Expression (CTE) computes the total number of bets, the total number of wins, and infers the losses. 2. We simultaneously compute expected wins and losses using a simple hypothesis of equal distribution. 3. The final `SELECT` statement computes the Chi-Squared statistic based on the observed and expected frequencies derived from `BettingData` and the hypothetical expected values. ### Notes: - Modify the logic of calculating `ExpectedWins` and `ExpectedLosses` based on your actual expected distribution. - NULLIF is used to prevent division by zero. - Ensure your categories match the expectations from your data (e.g., if multi-category then expand accordingly). This formula serves as a suitable guide, but you should ensure that assumptions about expected distributions align with your specific analysis objectives.