Understanding P-Values is essential for improving regression models.
In 2 minutes, I'll crush your confusion.
In 2 minutes, I'll crush your confusion.
1. The p-value:
A p-value in statistics is a measure used to assess the strength of the evidence against a null hypothesis.
A p-value in statistics is a measure used to assess the strength of the evidence against a null hypothesis.
2. Null Hypothesis (H₀):
The null hypothesis is the default position that there is no relationship between two measured phenomena or no association among groups. For example, under H₀, the regressor does not affect the outcome.
The null hypothesis is the default position that there is no relationship between two measured phenomena or no association among groups. For example, under H₀, the regressor does not affect the outcome.
3. Alternative Hypothesis (H₁):
The alternative hypothesis is what you want to test for and is typically the opposite of the null hypothesis. For example, under H₁, the regressor does affect the outcome.
The alternative hypothesis is what you want to test for and is typically the opposite of the null hypothesis. For example, under H₁, the regressor does affect the outcome.
4. Calculating the p-value:
In regression analysis, the p-value for each coefficient is typically calculated using a t-test. Several steps are involved in this process, which are outlined below.
In regression analysis, the p-value for each coefficient is typically calculated using a t-test. Several steps are involved in this process, which are outlined below.
5. Coefficient Estimate:
In a regression model, each predictor has an estimated coefficient (β) that represents the change in the dependent variable associated with a one-unit change in the predictor, assuming all other predictors remain constant.
In a regression model, each predictor has an estimated coefficient (β) that represents the change in the dependent variable associated with a one-unit change in the predictor, assuming all other predictors remain constant.
6. Standard Error of the Coefficient:
The standard error (SE) quantifies the precision of the coefficient estimate. A smaller SE indicates that the estimate is more precise, reflecting less variability in the estimate of the coefficient.
The standard error (SE) quantifies the precision of the coefficient estimate. A smaller SE indicates that the estimate is more precise, reflecting less variability in the estimate of the coefficient.
7. Test Statistic (T):
The test statistic for each coefficient is calculated by dividing the coefficient estimate by its standard error. This ratio yields a t-value that is used in the t-test.
The test statistic for each coefficient is calculated by dividing the coefficient estimate by its standard error. This ratio yields a t-value that is used in the t-test.
8. Degrees of Freedom:
The degrees of freedom (df) for the t-test are usually calculated as the number of observations minus the number of parameters being estimated (including the intercept).
The degrees of freedom (df) for the t-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 determined by comparing the calculated t-value to a t-distribution with the appropriate degrees of freedom. For a two-tailed test, it represents the probability of observing a t-value as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
The p-value is determined by comparing the calculated t-value to a t-distribution with the appropriate degrees of freedom. For a two-tailed test, it represents the probability of observing a t-value as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
10. Interpretation:
A small p-value (typically ≤ 0.05) indicates that the observed data pattern would be unlikely if the null hypothesis were true, suggesting that the predictor makes a statistically significant contribution to the model.
A small p-value (typically ≤ 0.05) indicates that the observed data pattern would be unlikely if the null hypothesis were true, suggesting that the predictor makes a statistically significant contribution to the model.
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