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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.
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)
What is the null hypothesis (H₀) in a t-test for slopes?
The null hypothesis assumes there is no relationship (or a specific relationship) between the variables. It's in the form H₀: β = β₀.
What is the alternative hypothesis (Hₐ) in a t-test for slopes?
The alternative hypothesis is what we're trying to find evidence for – that there is a relationship. It takes the form of Hₐ: β ≠ β₀, Hₐ: β < β₀, or Hₐ: β > β₀.
Define the t-statistic in the context of regression slope testing.
A measure of how far the sample slope is from the hypothesized slope (usually zero), in terms of standard errors. A large t-statistic suggests a significant relationship.
What does 'β' represent in the context of hypothesis testing for regression slopes?
β represents the population slope, the true change in the dependent variable for each unit increase in the independent variable.
What is a residual plot used for in regression analysis?
A residual plot is a graph that displays the residuals on the y-axis and the independent variable on the x-axis. It is used to assess the linearity and equal variance conditions of a regression model.