Question

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?

Short answer

a) The term for \(79 \%\) is the 'coefficient of determination' or \(R^{2}\). b) The response variable is the Hantavirus prevalence and the explanatory variable is the precipitation. c) The correlation between Hantavirus prevalence and precipitation is strong, but without additional information, we cannot specify if it is positive or negative.

Step-by-step solution

Identify the Term for the Value

The value of \(79 \%\) represents the degree to which the variation in the prevalence of Hantavirus can be explained by the variation in precipitation. In statistical language, this is known as the coefficient of determination, denoted as \(R^2\), which is obtained by squaring the correlation coefficient \(R\).

Identifying Response and Explanatory Variables

The response variable is the outcome variable on which we make observations. In this context, it's the prevalence of the Hantavirus. The explanatory variable, on the other hand, is the variable that might be influencing or causing changes in the response variable. Here, the explanatory variable is precipitation.

Determining the Correlation Between Variables

The \(R^2\) value given provides the percentage of variability in the response variable (Hantavirus prevalence) that is explained by the explanatory variable (precipitation). In this case, \(R^2 = 0.79\). To find \(R\) or the correlation coefficient, we take the square root of \(R^2\), which is approximately 0.89. However, we don't know the direction of the correlation (positive or negative) so we cannot definitively state the value of \(R\). Therefore, we can only say that the correlation is strong.