某作物的每公顷产量 $y$ kg 被认为取决于六月份的平均降雨量 $x$ mm。记录了 10 个地区的 $x$ 和 $y$ 值，如下表所示。数据分析后，第十个地区的产量不小心从记录中被删除了，该值用 $p$ 表示。

平均降雨量 ($x$ mm)	149	110	188	135	156	140	168	118	122	174
作物产量 ($y$ kg)	13.8	6.5	15.2	12.2	14.4	12.2	14.7	9.5	9.9	$p$

已知 $y$ 关于 $x$ 的回归直线方程为 $y = -2.5652 + 0.10168x$，证明 $p = 14.4$。

1. Calculate the sample mean of the average rainfall $x$, denoted as $\bar{x}$.

$\sum x = 149 + 110 + 188 + 135 + 156 + 140 + 168 + 118 + 122 + 174 = 1460$
$\bar{x} = \frac{1460}{10} = 146$

2. Find the sample mean of the yield $y$, $\bar{y}$, using the property that the regression line passes through the point $(\bar{x}, \bar{y})$.

Substitute $\bar{x} = 146$ into the given regression line equation $y = -2.5652 + 0.10168x$:
$\bar{y} = -2.5652 + 0.10168(146)$
$\bar{y} = -2.5652 + 14.84528 = 12.28008$

3. Set up an equation for $\bar{y}$ using the given dataset to solve for the missing value $p$.

Calculate the sum of the known $y$ values:
$\sum y_{\text{known}} = 13.8 + 6.5 + 15.2 + 12.2 + 14.4 + 12.2 + 14.7 + 9.5 + 9.9 = 108.4$
Using the formula for the mean $\bar{y} = \frac{\sum y}{n}$:
$\frac{108.4 + p}{10} = 12.28008$
$108.4 + p = 122.8008$
$p = 14.4008$
Rounding to 1 decimal place (consistent with the provided data), we obtain:
$p \approx 14.4 \text{ (shown)}$