AP Stats Inference for Slopes

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What is the null hypothesis (H0) in regression analysis?

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The null hypothesis (H0) states that there is no effect or no relationship between the variables, often expressed as b1 = 0.

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What does a p-value indicate in hypothesis testing?

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A p-value indicates the probability of observing the data, or something more extreme, if the null hypothesis is true. A low p-value (typically < 0.05) suggests rejecting the null hypothesis.

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What is the significance level in hypothesis testing?

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The significance level (alpha) is the threshold for determining whether to reject the null hypothesis, commonly set at 0.05.

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What is a regression equation?

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A regression equation is a mathematical representation of the relationship between independent and dependent variables, typically in the form: Y = a + bX.

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What does the slope (b1) in a regression equation represent?

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The slope (b1) represents the average change in the dependent variable (Y) for each one-unit increase in the independent variable (X).

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What is a residual in regression analysis?

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A residual is the difference between the observed value and the predicted value of the dependent variable.

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What does a residual plot show?

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A residual plot displays the residuals on the vertical axis and the independent variable on the horizontal axis, helping to assess the fit of the regression model.

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What does it mean if a residual plot shows a non-random pattern?

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A non-random pattern in a residual plot suggests that the regression model may not be appropriate, indicating a potential non-linear relationship.

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What is the purpose of the least squares method in regression?

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The least squares method minimizes the sum of the squares of the residuals, providing the best-fitting line for the data.

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What is the interpretation of the y-intercept (a) in a regression equation?

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The y-intercept (a) represents the predicted value of the dependent variable (Y) when the independent variable (X) is zero.