All Flashcards
What are the differences between the null and alternative hypotheses?
Null Hypothesis: Assumes no effect or relationship. | Alternative Hypothesis: Claims an effect or relationship exists.
Explain the concept of statistical significance in the context of regression slopes.
Statistical significance means that the observed relationship between the variables in the sample is unlikely to have occurred by random chance alone, suggesting a real relationship exists in the population.
Explain why we test if the slope (β) is different from zero.
Testing if β ≠ 0 determines if there's a meaningful linear relationship between the variables. If β = 0, there's no linear association.
Explain the importance of checking conditions before conducting a t-test for slopes.
Checking conditions ensures that the assumptions underlying the t-test are met, which validates the reliability and accuracy of the test results and conclusions.
Explain the implication of a non-linear pattern in the residual plot.
A non-linear pattern in the residual plot suggests that a linear model is not appropriate for the data, and a different type of model might be needed.
Explain the implication of unequal variance in the residual plot.
Unequal variance (fanning) in the residual plot violates the assumption of homoscedasticity, which can lead to inaccurate standard errors and unreliable test results.
What is the general form of the null hypothesis for the slope?
H₀: β = β₀, where β₀ is the hypothesized slope value.
Give the forms of the alternative hypothesis for the slope.
Hₐ: β ≠ β₀ (two-tailed), Hₐ: β < β₀ (left-tailed), or Hₐ: β > β₀ (right-tailed)