carter decides to research the relationship between the length in inches and the weight of a certain species…

carter decides to research the relationship between the length in inches and the weight of a certain species of catfish. he measures the length and weight of a number of specimens he catches, then throws back into the water. after plotting all his data, he draws a line of best fit. based on the line of best fit, what would you predict to be the length of a catfish that weighed 60 pounds?

carter decides to research the relationship between the length in inches and the weight of a certain species of catfish. he measures the length and weight of a number of specimens he catches, then throws back into the water. after plotting all his data, he draws a line of best fit. based on the line of best fit, what would you predict to be the length of a catfish that weighed 60 pounds?

Answer

Explanation:

Step1: Encontrar la pendiente de la línea

Usamos dos puntos en la línea de mejor ajuste, por ejemplo, ((20, 15)) y ((24, 24)). La fórmula de la pendiente (m) es (m=\frac{y_2 - y_1}{x_2 - x_1}). Sustituyendo, (m=\frac{24 - 15}{24 - 20}=\frac{9}{4}=2.25).

Step2: Escribir la ecuación de la línea

Usamos la forma punto - pendiente (y - y_1=m(x - x_1)) con el punto ((20, 15)). Entonces (y - 15 = 2.25(x - 20)). Simplificando: (y=2.25x-45 + 15=2.25x-30).

Step3: Predecir la longitud para (y = 60)

Sustituimos (y = 60) en la ecuación: (60=2.25x-30). Resolviendo para (x): (2.25x=60 + 30=90), entonces (x=\frac{90}{2.25}=40).

Answer:

40