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Understanding P-Values is essential for improving regression models. In 2 minutes, learn what took me 2 years to figure out.
1. The p-value: A p-value, in statistics, is a measure used to assess the strength of the evidence against a null hypothesis.
2. Null Hypothesis (H0): This is a general statement or default position that there is no relationship between two measured phenomena or no association among groups. For example, the regressor does not affect the outcome.
3. Alternative Hypothesis (H1): This is what you want to test for. It is often the opposite of the null hypothesis. For example, that the regressor does affect the outcome.
4. Calculating the p-value: The p-value for each coefficient is typically calculated using the t-test. There are several steps involved. Let's break them down.
5. Coefficient Estimate: In a regression model, you have estimates of coefficients (β) for each predictor. These coefficients represent the change in the dependent variable for a one-unit change in the predictor, holding all other predictors constant.
6. Standard Error of the Coefficient: The standard error (SE) measures the accuracy with which a sample represents a population. In regression, the SE of a coefficient estimate indicates how much variability there is in the estimate of the coefficient.
7. Test Statistic (T): The test statistic for each coefficient in a regression model is calculated by dividing the Coefficient Estimate / Standard Error of the Coefficient. This gives you a t-value.
8. Degrees of Freedom: The degrees of freedom (df) for this test are usually calculated as the number of observations minus the number of parameters being estimated (including the intercept).
9. P-Value Calculation: The p-value is then determined by comparing the calculated t-value to the t-distribution with the appropriate degrees of freedom. The area under the t-distribution curve, beyond the calculated t-value, gives the p-value.
10. Interpretation: A small p-value (usually ≤ 0.05) indicates that it is unlikely to observe such a data pattern if the null hypothesis were true, suggesting that the predictor is a significant contributor to the model.
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