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Fire damage in the United States amounts to billions of dollars, much of it insured. The time taken to arrive at the fire is critical. This raises the question, Should insurance companies lower premiums if the home to be insured is close to a fire station? To help make a decision, a study was undertaken wherein a number of fires were investigated. The distance to the nearest fire station (in miles) and the percentage of fire damage were recorded. Determine the least squares line and interpret the coefficients

Solution

VerifiedThe goal of this task is to use the values we are given in the excel table. We are given $85$ different values of the distance between the home and the closest fire station and $85$ different values for the percentage of the recorded damage resulting from the fire, which means the sample mean will amount to $85$, $n$ is $85$. In this case, the percentage of the recorded damage from the fire will be a dependent variable, $y$ and the distance between the home and the closest fire station will be an independent variable $x$. Using the given data we have to determine the regression line and conclude the relationship between the described distance and the percentage of recorded damage from fire.

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