Question

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

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