Roger is measuring the length of a hanging spring as various weights are added to it. Using these measurements, he obtained the following regression equation: y = 0.006x + 11.5, where y is the length of the spring in centimeters and x is the mass added to the spring in grams.

What is the meaning of the coefficient 0.006 in this equation?

a.) the stretch of the spring by a weight of 1 gram is 0.006 times of that caused by a weight of 11.5 grams

b.) the length of the spring increases by 0.006 cm for every gram added to it

c.) a weight of 6 grams stretches the spring by 1 cm

d.) a weight of 11.5 grams stretches the sprin by 0.006 cm

Question

Mathematics

Michelle Beck

25 November, 22:45

Roger is measuring the length of a hanging spring as various weights are added to it. Using these measurements, he obtained the following regression equation: y = 0.006x + 11.5, where y is the length of the spring in centimeters and x is the mass added to the spring in grams.

What is the meaning of the coefficient 0.006 in this equation?

a.) the stretch of the spring by a weight of 1 gram is 0.006 times of that caused by a weight of 11.5 grams

b.) the length of the spring increases by 0.006 cm for every gram added to it

c.) a weight of 6 grams stretches the spring by 1 cm

d.) a weight of 11.5 grams stretches the sprin by 0.006 cm

+1

Answers (1)

Know the Answer?

Renee · Answer 1

B.) the length of the spring increases by 0.006 cm for every gram added to it.

y = 0.006x + 11.50

where:

y = length of the spring in centimeters

x = mass added to the spring in grams

11.50 = the first number in the sequence

0.006 = the common difference among numbers in the sequence.

x y

1 11.5 + 0.006 (1) = 11.50 + 0.006 = 11.506

2 11.5 + 0.006 (2) = 11.50 + 0.012 = 11.512

3 11.5 + 0.006 (3) = 11.50 + 0.018 = 11.518

4 11.5 + 0.006 (4) = 11.50 + 0.024 = 11.524

5 11.5 + 0.006 (5) = 11.50 + 0.030 = 11.530

For every 1 gram added, the length of the string increases by 0.006cm