Topic 9: Graphing Polynomial Functions
Compute the least-squares regression line for predicting the ribeye price from the corn price.
One of the primary feeds for beef cattle is com. The following table presents the average price in dollars for a bushel of com and a pound of ribeye steak for 10 consecutive months.
\begin{tabular}{|cc|}
\hline Corn Price $(\$ / \mathrm{bu})$ & Ribeye Price $(\$ / \mathrm{b})$ \\
\hline 6.67 & 14.42 \\
5.75 & 11.90 \\
6.06 & 12.35 \\
5.92 & 12.62 \\
6.36 & 13.01 \\
6.13 & 13.27 \\
\hline
\end{tabular}

Step 1 ：First, we need to input the data. We can do this by creating two lists, one for the corn prices and one for the ribeye prices. The corn prices are [6.67, 5.75, 6.06, 5.92, 6.36, 6.13] and the ribeye prices are [14.42, 11.90, 12.35, 12.62, 13.01, 13.27].

Step 2 ：Then, we calculate the necessary sums and the number of data points. The number of data points (N) is 6, the sum of the corn prices (sum_X) is 36.89, the sum of the ribeye prices (sum_Y) is 77.57, the sum of the product of the corn and ribeye prices (sum_XY) is 478.2465, and the sum of the square of the corn prices (sum_X2) is 227.3479.

Step 3 ：Next, we calculate the slope (m) and the y-intercept (b) of the least-squares regression line. The slope (m) is \( \frac{N \cdot sum\_XY - sum\_X \cdot sum\_Y}{N \cdot sum\_X2 - sum\_X^2} = 2.463751438435031 \) and the y-intercept (b) is \( \frac{sum\_Y - m \cdot sum\_X}{N} = -2.219631760644719 \).

Step 4 ：Finally, we can write the equation of the least-squares regression line for predicting the ribeye price from the corn price. The equation is \( y = mx + b \), so the final answer is \( \boxed{y = 2.46x - 2.22} \).