Question

Consider the given data:

x & : 2, 4, 6, 7, 10, 11, 14, 17, 20
y & : 4, 5, 6, 5, 8, 8, 6, 9, 12
endalign*
Derive the least-squares fit of the following model: ( y = mx + b ).
a) ( y = 0.6x + 3 )
b) ( y = 0.8x + 2 )
c) ( y = 1.2x - 1 )
d) ( y = 1.5x - 2 )

Answer 1

To derive the least-squares fit of the given model y = mx + b, calculate the values of m and b using the provided formulas. Substituting the sums of the median x and y values and the slope, we find that the least-squares fit of the model is y = 0.09x + 35.25.

Step-by-step explanation:

To derive the least-squares fit of the given model, we need to find the values of m and b in the equation y = mx + b. We can use the formulas provided to calculate these values. The sum of the median x values is 1264 and the sum of the median y values is 219.5. Substituting these sums and the slope into the formula gives b = 219.5 - 0.09(1264), which simplifies to b ≈ 35.25. Therefore, the least-squares fit of the model is y = 0.09x + 35.25.