posted by Kimberly on .
The eggs of a species of bird have an average diameter of 23 mm and an SD of 0.45 mm. The weights of the chicks that hatch from these eggs have an average of 6 grams and an SD of 0.5 grams. The correlation between the two variables is 0.75 and the scatter diagram is roughly football shaped.
Find the regression estimate of the weight of a chick that hatches from an egg 24 mm in diameter.
Find the regression estimate of the weight of a chick that hatches from an egg 22.5 mm in diameter.
Eggs(x): mean = 23, sd = 0.45
Weights of chicks(y): mean = 6, sd = 0.5
Correlation: r = 0.75
Regression equation is in this format:
predicted y = a + bx
...where a = intercept and b = slope.
To find the equation, you need to substitute the information given in the problem into a workable formula:
predicted y = (rSy/Sx)X - (rSy/Sx)xbar + ybar
...where r = correlation, Sy = sd of y, Sx = sd of x, and X is the variable in 'a + bx' equation.
Note: xbar = mean of x; ybar = mean of y.
I'll let you take it from here. (Once you calculate the predicted y formula, substitute 24 and 22.5 for x in the formula to predict weights of the chicks.)
How do you find the intercept?