Suppose we add humans to the data in Problem 24 . Humans...

Suppose we add humans to the data in Problem $24 .$ Humans have a gestation period of 268 days and a life expectancy of 76.5 years. (a) Redraw the scatter diagram with humans included. (b) Recompute the linear correlation coefficient with humans included. (c) Compare the results of (a) and (b) with the results of Problem $24 .$ Provide a statement that explains the results.

Suppose we add humans to the data in Problem $24 .$ Humans have a gestation period of 268 days and a life expectancy of 76.5 years.
(a) Redraw the scatter diagram with humans included.
(b) Recompute the linear correlation coefficient with humans included.
(c) Compare the results of (a) and (b) with the results of Problem $24 .$ Provide a statement that explains the results.

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Key Concepts

Scatter Diagram

A scatter diagram is a graphical tool used to display the relationship between two quantitative variables on a Cartesian plane. It helps in visualizing patterns, trends, or clusters in the data, and can provide early insight into the type of relationship (linear, non-linear, or no clear association) that may exist between the variables.

Linear Correlation Coefficient

The linear correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where values near 1 indicate a strong positive linear relationship, values near -1 indicate a strong negative linear relationship, and values around 0 suggest little to no linear association.

Influential Data Points

Influential data points are observations that significantly impact statistical calculations such as the correlation coefficient or the regression line. When an additional data point, especially one that lies far from the main cluster of data, is introduced, it can alter the overall analysis, sometimes leading to different interpretations of the relationship between the variables.

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