Question

interpret the least squares regression line of this data set. every summer, the dayton fair has a grass - hopper catching contest. grasshoppers are released into a fenced area, and participants are given five minutes to catch as many as they can. to even the playing field, the organizers developed a handicap system based on the results of this years competition. the system takes into account the different experience levels of the contest participants. to create the system, the organizers recorded the number of times each contestant had previously participated, x, and the number of grasshoppers each contestant had caught this year, y. the correct least squares regression line for the data set is: y = 1.571x + 15.667. use it to complete the following sentence: the least squares regression line predicts that a participant would have caught blank more grasshoppers for each additional year of participation.

Explanation:

Step1: Identificar la pendiente de la ecuación

La ecuación de la recta de regresión lineal es $y = 1.571x+15.667$, donde la pendiente es $m = 1.571$.

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 el número de años de participación y $y$ es el número de saltamontes capturados. Entonces, por cada año adicional de participación, el número de saltamontes capturados aumenta en 1.571.

Answer:

1.571