Question

country	stork pairs(102)	birth rate (104/year)
Albania	1	8
Austria	3	9
Greece	25	11
Portugal	15	12
Romania	50	35
Spain	80	45

e) Calculate all the predicted values for the predicted variable (birth rate) for given values of the predictor variable (the number of stork pairs) in the data set.

f) On the scatterplot you constructed in (a), draw the regression line using the actual X and predicted Y scores (Y’).

Answer 1

X	y	(x-xbar)^2	(x-xbar)(y-ybar)
1 3 25 15 50 80	8 9 11 12 35 45	784 676 16 196 441 2601 SS: 4714	336 286 36 112 315 1275 SP: 2360

A) predicted equation

Sum of X = 174
Sum of Y = 120
Mean X = 29
Mean Y = 20
Sum of squares (SS_X) = 4714
Sum of products (SP) = 2360

Regression Equation = ŷ = bX + a

b = SP/SS_X = 2360/4714 = 0.50064

a = M_Y - bM_X = 20 - (0.5*29) = 5.48154

ŷ = 0.50064X + 5.48154

B) scatter plot