Which of the following statements is true?

Question

BlackTom AI · Accepted Answer

The question asks which statement is true, but the provided data lacks the set of answer options to compare. Nonetheless, we can analyze the single statement given for its general truth and clarify under what conditions it holds.

Statement under scrutiny: "The same two continuously measured variables can be used in correlation analysis or simple linear regression analysis."

Consider correlation analysis first: when you have two continuous variables X and Y, you can compute a correlation coefficient (such as Pearson's r) to assess the strength and direction of the linear relationship between them. This use is appropriate as long as the relationship is roughly linear and the data meet the standard assumptions (e.g., bivariate normality for Pearson correlation, homoscedasticity, and independence of observations where applicable).

Now consider simple linear regression: you can model Y as a function of X using Y = a + bX + error. This requires two continuous variables as inputs (the predictor X and the response Y) and is a standard application for these variables. The same pair (X, Y) can indeed be used to fit a regression line, interpret the slope as the change in Y per unit change in X, and assess goodness-of-fit with metrics like R-squared.

Therefore, from a theoretical standpoint, the statement is true in typical statistical practice. The caveats to keep in mind include: ensuring the variables are measured appropriately, recognizing that correlation does not imply causation, checking that the assumptions of linearity and homoscedasticity are reasonable for regression, and being aware that different analyses may require different handling of outliers or nonlinearity.

If there were additional options, one would compare them to this statement to determine which is most consistent with statistical principles. However, given only this option, its content aligns with standard usage of two continuous variables in both correlation and simple linear regression analyses.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 1A

Which of the following statements is true?

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Which one of the following statements is true?

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