The average time a chicken is typically incubated inside of its egg is 504 hours. Jacqueline studied 15 different baby chickens and documented the amount of time they were in the egg before it hatched and the weight of each one. Her data is shown on the graph with a line fit to the data to model the relationship between the weight of a baby chicken, y, in grams, and the amount of time it spent in the egg, x in hours.

The screen shot shows the slope, y-intercept, and correlation coefficient associated with the linear relationship modeled.
Complete the statements.
The equation for the line of best fit is

.
Using the model, the average number of hours of incubation of a chicken that weighs 25 ounces is approximately ___hours.
The correlation coefficient suggests there is a
,
association between the number of weeks gestation and the weight of a baby chicken

1 answer

To complete the statements, we will need some assumptions and standard values usually seen in these contexts. Since you have not provided the specific values of the slope, y-intercept, or the correlation coefficient, I will use placeholder variables.

  1. The equation for the line of best fit is \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. You should replace \( m \) and \( b \) with the actual values from Jacqueline's study.

  2. Using the model, the average number of hours of incubation of a chicken that weighs 25 ounces is approximately ___ hours. To find the average number of hours of incubation for a chicken that weighs 25 ounces, you would substitute \( y = 25 \) into the equation. Assuming you have the equation: \[ 25 = mx + b \] Rearranging to solve for \( x \): \[ x = \frac{25 - b}{m} \] You would need to replace \( 25 \), \( b \), and \( m \) with the appropriate values to find \( x \).

  3. The correlation coefficient suggests there is a __ association between the number of weeks gestation and the weight of a baby chicken. If the correlation coefficient (let’s say it's \( r \)) is close to 1 or -1, it suggests a strong linear association; if it’s close to 0, it suggests a weak association. If \( r \) is positive, it indicates a positive relationship, while a negative \( r \) indicates a negative relationship. So you might say:

    • If \( r > 0 \) and is close to 1, then: "The correlation coefficient suggests there is a strong positive association."
    • If \( r < 0 \) and is close to -1, then: "The correlation coefficient suggests there is a strong negative association."
    • If \( |r| \) is close to 0, then: "The correlation coefficient suggests there is a weak association."

Make sure to input and adjust these based on Jacqueline's actual data.