[{"id":"162b5bff-baae-4fd0-b198-1ca2e32aed46","public":true,"title":"Baysian Statistics","description":"A quick recap","created_at":"2025-12-10T16:03:45.654927","updated_at":"2025-12-10T20:41:04.733873","user_id":{"id":"53b2630f-c51e-41c1-a20c-1bb55d33d1d4","quizs":[{"id":"162b5bff-baae-4fd0-b198-1ca2e32aed46","public":true,"title":"Baysian Statistics","description":"A quick recap","created_at":"2025-12-10T16:03:45.654927","updated_at":"2025-12-10T20:41:04.733873","user_id":{"id":"53b2630f-c51e-41c1-a20c-1bb55d33d1d4"},"questions":[{"question":"What is the range of Bayesian probability?","time":"20","type":"ABCD","answers":[{"right":false,"answer":"-1 to 1","color":"#31a6eb"},{"right":true,"answer":"0 to ∞","color":"#eb8a31"},{"right":false,"answer":"-∞ to ∞","color":"#76eb31"},{"right":false,"answer":"0 to 1","color":"#e831eb"}],"image":null,"hide_results":false},{"question":"What is the core formula for the Bayesian Posterior distribution?","time":"35","type":"ABCD","answers":[{"right":false,"answer":"Posterior ∝ Likelihood + Prior","color":"#31a6eb"},{"right":false,"answer":"Posterior ∝ Likelihood / Prior","color":"#76eb31"},{"right":false,"answer":"Posterior ∝ Prior - Likelihood","color":"#eb9e31"},{"right":true,"answer":"Posterior ∝ Likelihood × Prior","color":"#e831eb"}],"image":null,"hide_results":false},{"question":"What is the formula for the Bayesian probability?","time":"20","type":"ABCD","answers":[{"right":false,"answer":"P(B|A) = (P(A) * P(B)) / P(A|B)","color":"#31a6eb"},{"right":true,"answer":"P(A|B) = (P(B|A) * P(A)) / P(B)","color":"#eb9e31"},{"right":false,"answer":"P(A|B) = (P(B) * P(A)) / P(B|A)","color":"#76eb31"},{"right":false,"answer":" P(B|A) = (P(A|B) * P(B)) / P(A)","color":"#e831eb"}],"image":null,"hide_results":false},{"question":"he pink line represents the posterior mode. Which Loss Function does this estimator minimize?","time":"20","type":"ABCD","answers":[{"right":true,"answer":"Zero-One Loss","color":"#31a6eb"},{"right":false,"answer":"Quadratic Loss","color":"#eb9e31"},{"right":false,"answer":"Absolute Loss","color":"#76eb31"},{"right":false,"answer":"Infinite Loss","color":"#e831eb"}],"image":"15f11b502940490880ea09ab8ead45d0","hide_results":false},{"question":"What does the likelihood function in Bayesian probability do?","time":"27","type":"ABCD","answers":[{"right":false,"answer":"It calculates the probability of prior knowledge","color":"#31a6eb"},{"right":true,"answer":"It updates the prior probability based on new evidence","color":"#eb9e31"},{"right":false,"answer":"It eliminates uncertainties completely","color":"#76eb31"},{"right":false,"answer":"It determines the absolute probability of an event","color":"#e831eb"}],"image":null,"hide_results":false},{"question":"Both analyses estimated the same mean (𝜇=5), but Analysis B (Green) is much narrower/sharper. 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Which Loss Function does this estimator minimize?","time":"20","type":"ABCD","answers":[{"right":true,"answer":"Zero-One Loss","color":"#31a6eb"},{"right":false,"answer":"Quadratic Loss","color":"#eb9e31"},{"right":false,"answer":"Absolute Loss","color":"#76eb31"},{"right":false,"answer":"Infinite Loss","color":"#e831eb"}],"image":"15f11b502940490880ea09ab8ead45d0","hide_results":false},{"question":"What does the likelihood function in Bayesian probability do?","time":"27","type":"ABCD","answers":[{"right":false,"answer":"It calculates the probability of prior knowledge","color":"#31a6eb"},{"right":true,"answer":"It updates the prior probability based on new evidence","color":"#eb9e31"},{"right":false,"answer":"It eliminates uncertainties completely","color":"#76eb31"},{"right":false,"answer":"It determines the absolute probability of an event","color":"#e831eb"}],"image":null,"hide_results":false},{"question":"Both analyses estimated the same mean (𝜇=5), but Analysis B (Green) is much narrower/sharper. 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(Hint: alpha-value=0.05)","time":"30","type":"ABCD","answers":[{"right":false,"answer":"x1","color":"#31a6eb"},{"right":false,"answer":"x2","color":"#76eb31"},{"right":false,"answer":"x3","color":"#eb9e31"},{"right":true,"answer":"x4","color":"#e831eb"}],"image":"425050d2-179a-4727-9a6b-9112e1190c4f","hide_results":false},{"question":"What is the correct interpretation of R-squared = 0.9637?","time":"30","type":"ABCD","answers":[{"right":false,"answer":"96.37% of the data points fall on the regression line","color":"#31a6eb"},{"right":false,"answer":"There is a 96.37% probability that X influences Y","color":"#76eb31"},{"right":true,"answer":"96.37% of the variance in Y is explained by the regression model","color":"#eb9e31"},{"right":false,"answer":"The model makes correct predictions 96.37% of the time","color":"#e831eb"}],"image":"16dd2824-b4d3-4d91-bb05-3c099c8aaefb","hide_results":false},{"question":"Comparing the two regression models below, which model is BETTER?","time":"35","type":"ABCD","answers":[{"right":false,"answer":"Model 1","color":"#31a6eb"},{"right":true,"answer":"Model 2","color":"#76eb31"}],"image":"9669af17-ddb5-46d2-be4c-5b2d68188835","hide_results":false},{"question":"What is t hedifference between R-squared and ADJUSTED R-squared?","time":"30","type":"ABCD","answers":[{"right":false,"answer":"-squared measures linearity, Adjusted R-squared measures non-linearity","color":"#31a6eb"},{"right":false,"answer":"R-squared measures prediction accuracy, Adjusted R-squared measures causality","color":"#76eb31"},{"right":true,"answer":"R-squared always increases with more variables, Adjusted R-squared penalizes unnecessary complexity","color":"#eb9e31"},{"right":false,"answer":"R-squared is for small samples, Adjusted R-squared is for large samples","color":"#e831eb"}],"image":"ce2fd80e-4895-4136-9562-6c0ff7b09569","hide_results":false},{"question":"What is heteroskedasticity?","time":"30","type":"ABCD","answers":[{"right":false,"answer":"When residuals are not normally distributed","color":"#31a6eb"},{"right":false,"answer":"When predictors are correlated with each other","color":"#76eb31"},{"right":true,"answer":"When the variance of residuals is not constant","color":"#eb9e31"},{"right":false,"answer":"When the regression line is curved","color":"#e831eb"}],"image":"1d7d015b-f45e-4239-addd-7ff5919d7b29","hide_results":false},{"question":"What is the opposite of heteroskedasticity?","time":"30","type":"ABCD","answers":[{"right":false,"answer":"Multicollinearity","color":"#31a6eb"},{"right":true,"answer":"Homoskedasticity","color":"#76eb31"},{"right":false,"answer":"Autocorrelation","color":"#eb9e31"},{"right":false,"answer":"Normality","color":"#e831eb"}],"image":"1e0f99cd-984c-427b-aba3-2292ddb7d7d3","hide_results":false},{"question":"Based on the regression output below, which is the correct final model description? 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@classy

Baysian Statistics

Linear Regression