In Exercises 39-44, plot the points and determine whether...

In Exercises $39-44,$ plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of $r$ and confirm your result. The number $r$ is called the correlation confficient. It is a measure of how well the model fits the data. Correlation coefficients vary between $-1$ and $1,$ and the closer $|r|$ is to $1,$ the better the model. (GRAPH NOT COPY) Positive correlation Negative correlation No correlation $$ (1,4),(2,6),(3,8),(4,11),(5,13),(6,15) $$

In Exercises $39-44,$ plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of $r$ and confirm your result. The number $r$ is called the correlation confficient. It is a measure of how well the model fits the data. Correlation coefficients vary between $-1$ and $1,$ and the closer $|r|$ is to $1,$ the better the model.
(GRAPH NOT COPY)
Positive correlation Negative correlation No correlation
$$
(1,4),(2,6),(3,8),(4,11),(5,13),(6,15)
$$

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Key Concepts

Correlation Coefficient

The correlation coefficient, denoted as r, is a numerical measure that quantifies the strength and direction of the linear relationship between two variables. Its value ranges from -1 to 1; values closer to 1 indicate a strong positive linear correlation, values closer to -1 indicate a strong negative linear correlation, and values around 0 suggest little to no linear relationship.

Scatter Plot

A scatter plot is a type of graph used to display values for typically two variables for a set of data. Each point on the graph represents an observation with its coordinates marking values from each variable, allowing visual assessment of any pattern, trend, or relationship between them.

Linear Correlation

Linear correlation refers to the relationship between two variables where the association can be approximated by a straight line. It assesses whether increases in one variable correspond to increases or decreases in another variable in a predictable manner.

Positive Correlation

Positive correlation occurs when an increase in one variable is associated with an increase in another variable, resulting in an upward trend on a scatter plot. This indicates that as one variable grows, the other tends to grow as well, suggesting a direct linear relationship.

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