Question

A limnologist takes samples from a creek on several days

and counts the numbers of flatworms in each sample,

The limnologist wants to look at the relationship between

the temperature of the creek and the number of

flatworms in the sample. The data show a linear pattern

with the summary statistics shown below:

mean

standard

deviation

= 10.2

Sx = 2.8

x = creek temperature

(C)

j = 37.6

$y = 30.8

y = number of

flatworms

• = -0.98

Find the equation of the least-squares regression line

for predicting the number of flatworms from the

creek temperature.

Round your entries to the nearest hundredth.

Answer 1

y = 147.56 + -10.78x

Explanation:

Answer 2

y = 147.56 - 10.78x

Explanation:

Given :

x = 10.2 ; y = 37.6 ; Sx = 2.8 ; Sy = 30.8 ; r = - 0.98

The regression equation :

y = mx + c

Where ;

m = slope ; c = intercept

Slope = r * (Sy/Sx)

Slope = - 0.98 * (30.8 / 2.8)

Slope = - 0.98 * 11 = - 10.78

To obtain c :

y = mx + c

y - mx = c

37.6 - (-10.78)(10.2) = c

37.6 + 109.956 = c

147.556 = c

Hence, equation becomes :

y = 147.556 - 10.78x

y = 147.56 - 10.78x