Question

Data from a random sample of 11 gravid female iguanas, including their postpartum weights and the number of eggs each produced, were collected.

(1): Construct a two-way scatter plot for “female mass” against the “number of eggs” and on a separate graph construct a two-way scatter plot for “female mass” against log of the “number of eggs”. Looking at the two graphs you plotted, explain as to which of these two do you consider to be closest to a linear relationship?

(2): Compute r, the Pearson correlation coefficient

(3): Compute and use the regression equation you came up with in the previous part (namely “f”) to predict the “number of eggs” for and “female mass” of 2 kg.

Specimen	Mass (kg)	Number of eggs
1	0.90	33
2	1.55	50
3	1.30	46
4	1.00	33
5	1.55	53
6	1.80	57
7	1.50	44
8	1.05	31
9	1.70	60
10	1.20	40
11	1.45	50

Answer 1

a.

b.

X Values
∑ = 15
Mean = 1.364
∑(X - M_x)² = SS_x = 0.875

Y Values
∑ = 497
Mean = 45.182
∑(Y - M_y)² = SS_y = 993.636

X and Y Combined
N = 11
∑(X - M_x)(Y - M_y) = 28.073

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 28.073 / √((0.875)(993.636)) = 0.9518

c.

Sum of X = 15
Sum of Y = 497
Mean X = 1.3636
Mean Y = 45.1818
Sum of squares (SS_X) = 0.8755
Sum of products (SP) = 28.0727

Regression Equation = ŷ = bX + a

b = SP/SS_X = 28.07/0.88 = 32.0665

a = M_Y - bM_X = 45.18 - (32.07*1.36) = 1.4548

ŷ = 32.0665X + 1.4548

For x=2, ŷ = (32.0665*2) + 1.4548=65.5878