During today’s class, we gained insights into the importance of p-values and the null hypothesis within the context of simple linear regression:
P-value Explanation: The p-value gauges the probability of observing the data as it is, assuming that the null hypothesis holds true. A low p-value indicates strong evidence against the null hypothesis.
Hypothesis Testing: We compare the p-value to a significance level, often set at 0.05. If p ≤ the significance level, we typically reject the null hypothesis and favor an alternative hypothesis.
Significance of the Null Hypothesis: The null hypothesis serves as the initial assumption, representing the absence of an effect or relationship between variables. Additionally, we delved into the concept of Standard Errors (SE), which quantify the precision of coefficient estimates and facilitate the computation of confidence intervals.
Confidence Intervals: Confidence intervals offer a range of values that are likely to encompass the true parameter value with a specified level of confidence, often 95%. We can employ hypothesis tests on coefficients, such as β1, to ascertain if there exists a statistically significant relationship between variables. A small standard error coupled with a corresponding t-statistic may indicate that the coefficient significantly differs from zero, implying the presence of a relationship.