Let be the SSE function for the best fitting line of the data below. A student calculated that the minimum of f occurs at . Based on this calculation, what is the linear function that best fits the data?

Question

Let  be the SSE function for the best fitting line  of the data below. A student calculated that the minimum of f occurs at  . Based on this calculation, what is the linear function that best fits the data?

Quizplus · Accepted Answer

The given SSE function is 11eaa894_6478_b58b_a158_e5d46d0b8027_TB6775_11, which corresponds to:
f(x) = 11eaa894_6478_b58c_a158_67f1f0bb2fec_TB6775_11 x + 11eaa894_6478_b58d_a158_cff860947ead_TB6775_11

To find the minimum of f, we need to differentiate f and set it equal to 0:
f'(x) = 11eaa894_6478_b58c_a158_67f1f0bb2fec_TB6775_11
11eaa894_6478_b58c_a158_67f1f0bb2fec_TB6775_11 x + 11eaa894_6478_b58d_a158_cff860947ead_TB6775_11 = 0
x = (11eaa894_6478_b58d_a158_cff860947ead_TB6775_11) / (-11eaa894_6478_b58c_a158_67f1f0bb2fec_TB6775_11)

Substituting this value of x in f(x), we get the best fitting line:
f(x) = 11eaa894_6478_b58c_a158_67f1f0bb2fec_TB6775_11 x + 11eaa894_6478_b58d_a158_cff860947ead_TB6775_11
= 11eaa894_6478_dca1_a158_afcb49bb442b_TB6775_11 x + 11eaa894_6478_dca2_a158_657c11af91de_TB6775_11

Therefore, the correct choice is C.

Let Be the SSE Function for the Best Fitting