Hantavirus is carried by wild rodents and causes severe lung...

Hantavirus is carried by wild rodents and causes severe lung disease in humans. A study $^{5}$ on the California Channel Islands found that increased prevalence of the virus was linked with greater precipitation. The study adds "Precipitation accounted for $79 \%$ of the variation in prevalence." (a) What notation or terminology do we use for the value $79 \%$ in this context? (b) What is the response variable? What is the explanatory variable? (c) What is the correlation between the two variables?

Hantavirus is carried by wild rodents and causes severe lung disease in humans. A study $^{5}$ on the California Channel Islands found that increased prevalence of the virus was linked with greater precipitation. The study adds "Precipitation accounted for $79 \%$ of the variation in prevalence."
(a) What notation or terminology do we use for the value $79 \%$ in this context?
(b) What is the response variable? What is the explanatory variable?
(c) What is the correlation between the two variables?

Key Concepts

Correlation Coefficient

The correlation coefficient is a measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values close to 1 indicate a strong positive relationship, values near -1 indicate a strong negative relationship, and values around 0 suggest little to no linear association. In contexts where the coefficient of determination (R²) is known, the correlation coefficient can be approximated by taking the square root of R², adjusting the sign based on the direction of the relationship.

Coefficient of Determination (R²)

The coefficient of determination is a statistical measure that represents the proportion of the variance in the response variable that can be explained by the explanatory variable in a regression model. It is expressed as a percentage—in this case, 79%—which indicates the strength of the association between the predictor and the outcome by showing how much variation the predictor accounts for in the response variable.

Response and Explanatory Variables

In statistical modeling, the response variable (or dependent variable) is the one being studied and is presumed to be influenced by other factors, while the explanatory variable (or independent variable) is the one thought to cause or predict changes in the response variable. Identifying these correctly is crucial to understanding the relationship being investigated, regardless of the specific context of the study.

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