ML EXPLAINED

Null Hypothesis of Linear Regression Explained

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sahaymaniceet

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Ever wondered why we look for p-value less than 0.05 for the coefficients when looking at the linear regression results.

Let’s quickly recap the basics of linear regression. In Linear Regression we try to estimate a best fit line for given data points. In case we have only one predictor variable and a target the linear equation will look something like

Y = A + Bx

Here A being the intercept and B being the slope or coefficient.

The null hypothesis for linear regression is that B=0 and the alternate hypothesis is that B != 0.

This is the reason why we look for p-value < 0.05 to reject the null hypothesis and establish that there exists a relationship between the target and the predictor variable.

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One response to “Null Hypothesis of Linear Regression Explained”

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    Anonymous

    Variables with p-values above 0.05 are often considered insignificant, meaning they might not have a meaningful impact on the response variable. Such variables may be candidates for removal during feature selection to simplify the model.

    Context Matters: The p-value should not be the sole criterion for deciding the relevance of a predictor. Domain knowledge, effect size, and confidence intervals are equally important.

    Multiple Testing: When testing many coefficients, the chance of false positives increases. Adjustments like the Bonferroni correction may be needed.

    Practical Significance vs. Statistical Significance: Even if a p-value is below 0.05, the effect size (coefficient magnitude) should be meaningful in practical terms.

    By using p<0.05, we aim to ensure that the predictors in our model are not only present by chance but are likely contributing significantly to explaining the variance in the dependent variable.

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