Λresearcher reported that the typical teenager needs 9.3...

$\Lambda$ researcher reported that the typical teenager needs 9.3 hours of sleep per night but gets only 6.3 hours. ${ }^{18} \mathrm{By}$ the end of a 5 -day school week, a teenager would accumulate about 15 hours of "sleep debt." Students in a high school statistics class were skeptical, so they gathered data on the amount of sleep debt (in hours) accumulated over time (in days) by a random sample of 25 high school students. The resulting least-squares regression equation for their data is Sleep debt $=2.23+3.17$ (days). (a) Interpret the slope of the regression line in context. (b) Are the students' results consistent with the rescarcher's report? Explain.

$\Lambda$ researcher reported that the typical teenager needs 9.3 hours of sleep per night but gets only 6.3 hours. ${ }^{18} \mathrm{By}$ the end of a 5 -day school week, a teenager would accumulate about 15 hours of "sleep debt." Students in a high school statistics class were skeptical, so they gathered data on the amount of sleep debt (in hours) accumulated over time (in days) by a random sample of 25 high school students. The resulting least-squares regression equation for their data is Sleep debt $=2.23+3.17$ (days). (a) Interpret the slope of the regression line in context.
(b) Are the students' results consistent with the rescarcher's report? Explain.

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Key Concepts

Comparing Empirical Findings with Established Research

This concept involves assessing whether the results derived from data analysis (such as estimates from a regression model) are consistent with established theories, expectations, or findings from previous research. This comparison helps in validating the results through a familiar benchmark and can indicate whether discrepancies should be further investigated or may be attributed to natural variability.

Interpretation of the Slope in Context

The slope of a regression line indicates the amount of change in the dependent variable associated with a one-unit change in the independent variable. This interpretation is crucial because it translates the numerical value of the slope into a meaningful context, showing how rapidly or slowly the outcome variable is expected to increase or decrease with each unit change.

Least-Squares Regression Analysis

This is a statistical technique used to model the linear relationship between a dependent variable and an independent variable by minimizing the sum of the squared differences between the observed and predicted values. It provides estimates for the slope and intercept, which form the regression equation used to predict outcomes.

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