A study on antibiotic use among children in Manitoba,...

A study on antibiotic use among children in Manitoba, Canada, gave the following data for the number of prescriptions per 1000 children $x$ years after 1995 CAN'T COPY THE TABLE (a) Draw a scatter diagram of the data, treating year as the explanatory variable. What type of relation, if any, appears to exist between year and antibiotic prescriptions among children? (b) Compute the linear correlation coefficient between year and antibiotic prescriptions among children. (c) Comment on the type of relation that appears to exist between year and antibiotic prescriptions among children on the basis of the scatter diagram and the linear correlation coefficient.

A study on antibiotic use among children in Manitoba, Canada, gave the following data for the number of prescriptions per 1000 children $x$ years after 1995
CAN'T COPY THE TABLE
(a) Draw a scatter diagram of the data, treating year as the explanatory variable. What type of relation, if any, appears to exist between year and antibiotic prescriptions among children?
(b) Compute the linear correlation coefficient between year and antibiotic prescriptions among children.
(c) Comment on the type of relation that appears to exist between year and antibiotic prescriptions among children on the basis of the scatter diagram and the linear correlation coefficient.

Key Concepts

Scatter Diagram

A scatter diagram is a graphical representation that plots paired data points with one variable on the horizontal axis (x-axis) and the other on the vertical axis (y-axis). This type of graph is used to visually assess the relationship, pattern, or trend between two quantitative variables, such as whether there appears to be any association, linear or non-linear, between them.

Explanatory Variable

The explanatory variable (or independent variable) is the variable that is presumed to affect or predict changes in another variable (the response variable). In data analysis and regression, accurately identifying the explanatory variable is crucial, as it is typically placed on the horizontal axis of a scatter plot and is used to forecast or explain variations in the response variable.

Linear Correlation Coefficient

The linear correlation coefficient, often denoted as 'r', measures the strength and direction of a linear relationship between two quantitative 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 close to 0 suggest little or no linear association.

Correlation Interpretation

Interpreting a scatter diagram alongside the linear correlation coefficient involves looking for patterns in the spread of the data points and quantifying their linear relationship. A clear clustering along an upward or downward sloping line, coupled with an 'r' value near +1 or -1, respectively, indicates a strong linear association. Conversely, a dispersed pattern without a clear trend and an 'r' value close to 0 denotes a weak or nonexistent linear relationship.

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