Question

maura has noticed that her bike ride to work takes longer on some days than others. she is curious to see how the morning temperature is related to the duration of her commute. for the past several mornings, she measured the temperature (in celsius), x, and the time her commute had taken (in minutes), y. the correct least squares regression line for the data set is: y = -2.222x + 51.758. use it to complete the following sentence: the least squares regression line indicates that mauras commute would be minutes shorter if the morning temperature increases one degree celsius.

Explanation:

Step1: Identificar la pendiente de la recta de regresión

La ecuación de la recta de regresión es $y = - 2.222x+51.758$, donde la pendiente es $m=-2.222$.

Step2: Interpretar la pendiente

En una ecuación lineal $y = mx + b$, la pendiente $m$ representa el cambio en $y$ por cada cambio unitario en $x$. Aquí, $x$ es la temperatura y $y$ es el tiempo de viaje. Entonces, por cada aumento de 1 grado Celsius en la temperatura ($x$ aumenta en 1), el tiempo de viaje $y$ disminuye en 2.222 minutos.

Answer:

2.222