Virtual Labs

What is the primary purpose of regression analysis in statistics?

a: To calculate the mean of a dataset. Explanation

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b: To model and analyze the relationship between a dependent variable and one or more independent variables, facilitating prediction and understanding of their associations. Explanation

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c: To find the mode of a dataset. Explanation

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d: To perform hypothesis testing. Explanation

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In a simple linear regression equation Y = β₀ + β₁X + ε, what does β₀ represent?

a: The error term. Explanation

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b: The slope of the line. Explanation

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c: The intercept (the value of Y when X is 0). Explanation

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d: The variance of the dataset. Explanation

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What does the coefficient of determination (R²) indicate in regression analysis?

a: It measures the strength of the relationship between the independent and dependent variables. Explanation

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b: It quantifies the proportion of the variance in the dependent variable that is predictable from the independent variables. Explanation

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c: It calculates the sum of squares of residuals. Explanation

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d: It determines the p-value of the regression equation. Explanation

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What are residuals in the context of regression analysis?

a: The independent variables in the regression equation. Explanation

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b: The predicted values of the dependent variable. Explanation

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c: The differences between the observed and predicted values of the dependent variable. Explanation

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d: The intercept of the regression equation. Explanation

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What is a key assumption in regression analysis regarding residuals?

a: Residuals must be perfectly correlated with the independent variables. Explanation

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b: Residuals should have a mean of zero. Explanation

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c: Residuals must be equal to the observed values. Explanation

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d: Residuals should follow a perfect linear pattern. Explanation

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Regression