Before data is entered into the regression calculator, some data may be excluded. Explain why the data pair (0, 100) was excluded for the comparison of hours slept the night before and the test score. Describe what this data point represents. If it was included, would the trend line describe the data well?

Answer 1

The data pair (0, 100) in the context of comparing hours slept the night before and test scores represents a scenario in which a participant reported having slept for 0 hours and achieved a test score of 100. This data point could be excluded for several reasons:

1. Outlier Status: This data point could be considered an outlier. Typically, we expect that more sleep correlates positively with higher test scores. A score of 100 with 0 hours of sleep is unusual and doesn't align with the general trend we would expect from the dataset.

2. Infeasibility and Realism: The scenario of achieving a perfect test score with no sleep at all is generally unrealistic. Most individuals would likely perform poorly without sleep due to fatigue, lack of focus, and diminished cognitive abilities.

3. Influencing the Trend Line: Including the (0, 100) data point could distort the regression analysis. It might falsely suggest that even with no sleep, one could achieve a perfect score, thereby weakening the correlation between hours slept and test scores. This could lead to a trend line that does not accurately represent the overall relationship in the data.

If this data point were included in the regression analysis, it would likely skew the results, making the trend line less representative of the actual data points. It could imply that there is a weaker or non-existent correlation between hours of sleep and test scores, which contradicts established understanding of the relationship. Over time, including such outliers might detract from the model's predictive ability and make it less reliable when applied to other, more typical instances.