Question

An ornithologist wants to look at the relationship between the breadth of

Deregrine falcon eggs and the mass of the falcon chicks that hatch from
them. The data show a linear pattern with the summary statistics shown
below:
mean
x = egg breadth (mm) = 41
y = chick's mass (g)
y = 33.6
standard deviation
82 = 2.3
Sy = 4.6
r = 0.95
Find the equation of the least-squares regression line for predicting the
chick's mass from the breadth of the egg.
Round your entries to the nearest hundredth.
y =
+
8

Answer 1

The equation of the least-squares regression line for predicting the chick's mass from the breadth of the egg is y = 1.9x - 44.9.

Step-by-step explanation:

The equation of the least-squares regression line for predicting the chick's mass from the breadth of the egg can be found using the formula:

y = bx + a

Where b is the slope and a is the y-intercept.

Given the summary statistics, we have:

mean x = 41

mean y = 33.6

standard deviation of x = 2.3

standard deviation of y = 4.6

correlation coefficient r = 0.95

To find the slope, we can use the formula:

b = r * (Sy / Sx)

Substituting the values, we get:

b = 0.95 * (4.6 / 2.3) = 1.9

To find the y-intercept, we can use the formula:

a = mean y - (b * mean x)

Substituting the values, we get:

a = 33.6 - (1.9 * 41) = -44.9

Therefore, the equation of the least-squares regression line is:

y = 1.9x - 44.9