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
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 fill in the statements, we would typically need the specific values for the slope, y-intercept, and correlation coefficient from Jacqueline's study. However, I can demonstrate how to complete the statements with hypothetical values. You can substitute the specific values from the screenshot you have.

  1. The equation for the line of best fit is: \[ y = mx + b \] (where \(m\) is the slope and \(b\) is the y-intercept). For example, if the slope is 0.5 grams per hour and the y-intercept is 20 grams, then the equation would be: \[ y = 0.5x + 20 \]

  2. Using the model, the average number of hours of incubation of a chicken that weighs ________ ounces is approximately ________ hours.
    (You would need to convert the weight in ounces to grams, since the model is in grams, and then solve for \(x\) using the equation from step 1). For example, if the weight is 7 ounces (which is approximately 198 grams), you would set \(y = 198\) and solve for \(x\): \[ 198 = 0.5x + 20 \implies 0.5x = 178 \implies x = 356 \text{ hours} \]

  3. The correlation coefficient suggests there is a ________, ________ association between the number of weeks gestation and the weight of a baby chicken. (You would interpret the correlation coefficient, which ranges from -1 to 1. If the coefficient is, for example, 0.8, you would say there is a strong, positive association. If it were -0.8, you would say there is a strong, negative association. If it were near 0, you might say there is a weak or negligible association).

If you can provide the specific values for the slope, y-intercept, correlation coefficient, and the weight in ounces, I can help you complete the statements accordingly!