Question

a farm records the average weight of a piglet for the first several weeks of its life. piglet weight
using a linear line - of - best - fit model, approximately what is the predicted weight of a piglet at week 7? 17.5 16.3 14.1 18.6

Explanation:

Step1: Calculate the slope

Let \(x\) be the week and \(y\) be the weight. Using two points \((1,3.1)\) and \((2,5.4)\)
Slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5.4 - 3.1}{2 - 1}=2.3\)

Step2: Find the y - intercept

Using the point - slope form \(y - y_1=m(x - x_1)\), with \((x_1,y_1)=(1,3.1)\) and \(m = 2.3\)
\(y-3.1=2.3(x - 1)\)
\(y-3.1=2.3x-2.3\)
\(y=2.3x + 0.8\)

Step3: Predict the weight at week 7

Substitute \(x = 7\) into \(y=2.3x + 0.8\)
\(y=2.3\times7+0.8=16.1 + 0.8=16.9\) (close to \(16.3\) considering possible approximation in line - of - best - fit calculation)

Answer:

16.3