IB MATH AI SL, Paper 1, November, 2021, TZ0, Solved Past Paper

Eduardo is investigating whether there is a linear relationship between the age of male runners and their performance in a 5000-meter race. To explore this, he collected data on the ages and corresponding race times of eight male participants. The data is presented in a table and visually represented in a scatter diagram. The aim is to determine if a linear correlation exists between the two variables, age and time, and to quantify this relationship using statistical methods.

Eduardo's data includes ages, denoted as \(x\), and race times, denoted as \(t\). The task involves calculating the Pearson's product-moment correlation coefficient, \(r\), which measures the strength and direction of the linear relationship between these variables. Additionally, Eduardo seeks to interpret the correlation coefficient using information from a sports science textbook, which categorizes the strength of correlations based on the absolute value of $r$.

Furthermore, the problem requires finding the equation of the regression line of $t$ on $x$ in the form $t=ax+b$. This equation models the relationship between age and race time, allowing predictions of race times for different ages. Finally, using the regression line equation, Eduardo estimates the race time for a 57-year-old male runner who participated in the same race.