Final answer:
The regression estimate (Y estimate) of the weight of a bird that hatches from an egg with a diameter of 24 mm is approximately 10.4 grams.
Step-by-step explanation:
To find the regression estimate (Y estimate) of the weight of a bird that hatches from an egg with a diameter of 24 mm, we can use the regression model. Given that the correlation between egg diameter and bird weight is 0.75, and the means and standard deviations of the variables are provided, we can calculate the regression equation.
The regression equation is given by: Y = bX + a, where Y is the weight of the bird, X is the diameter of the egg, and b and a are the slope and intercept of the regression line, respectively.
To calculate the slope, we can use the formula: b = r * (SD(y) / SD(x)), where r is the correlation coefficient, SD(y) is the standard deviation of the bird weight, and SD(x) is the standard deviation of the egg diameter.
To calculate the intercept, we can use the formula: a = mean(y) - b * mean(x), where mean(y) is the mean of the bird weight and mean(x) is the mean of the egg diameter.
Plugging in the values, we have:
Slope (b) = 0.75 * (0.4 / 0.5) = 0.6
Intercept (a) = 6 - 0.6 * 23 = -6.8
Therefore, the regression equation is: Y = 0.6X - 6.8
Substituting X = 24 into the equation, we get:
Y = 0.6 * 24 - 6.8 = 10.4
The regression estimate (Y estimate) of the weight of a bird that hatches from an egg with a diameter of 24 mm is approximately 10.4 grams.