Hooke's Law states that the length L of a spring is a linear function of the force F applied to it. (See Figure 7.1 7 and Example 6.92.) Accordingly, there are constants a and b such that
L = a + bF
Table 7.4 shows the results of attaching various weights to a spring.
Table 7.17

Table 7.4

(a) Determine the constants a and b by finding the least squares approximating line for these data. What does a represent?
(b) Estimate the length of the spring when a weight of 5 ounces is attached.

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Table 7.4 F (oz) 2 4 L(in.) 7.4 9.6 6 11.5 13.6