Question

The data given in Example \(5.5\) on \(x=\) call-to-shock time (in minutes) and \(y=\) survival rate (percent) were used to compute the equation of the least- squares line, which was $$ \hat{y}=101.36-9.30 x $$ The newspaper article "FDA OKs Use of Home Defibrillators" (San Luis Obispo Tribune, November 13,2002 ) reported that "every minute spent waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10 percent." Is this statement consistent with the given least-squares line? Explain.

Short answer

Yes, the statement is approximately consistent with the given least square line. While the line suggests a survival rate decrease of 9.3% per minute, the article indicates a 10% decrease per minute. The figures are similar, hence approximate consistency can be inferred.

Step-by-step solution

Understand the Least-Squares Line

The least-squares line \(\hat{y}=101.36 - 9.30x\) acts as a predictive model for survival rate based on the call-to-shock time. The coefficient of \(x\) (-9.30) is significant because it denotes the rate of decrease in survival percentage for each additional minute the defibrillator is delayed.

Examine the Newspaper Statement

According to the statement in the newspaper article, every minute delay in the arrival of defibrillators lowers survival rate by 10%. It implies a decrease of 10 units in survival rate per minute, which corresponds to an assumed linear model with a slope of -10.

Compare the Two Statements

The two statements can now be compared. The newspaper statement suggests a decrease in survival rate at a rate of 10% per minute, while the computed least squares line suggests a decrease at a rate of 9.30% per minute. Although these values are not exactly the same, they are very close, suggesting an approximate agreement between the two.