Step 1: Use the given equation to calculate the slope.

The least-squares regression line has the general form:

$y = a + bx$

Where:

• $a$ is the y-intercept.
• $b$ is the slope of the regression line.

Given that the y-intercept $a = -99.2105263157895$, we need to compute the slope $b$. We will apply the least-squares formula, but only the x-values ($x = [178, 176, 174, 166, 172, 172, 174]$) are provided. To proceed, we need the $y$-values or additional details, which are not given in this problem.

Step 2: Predict the value of $y$ using the hypothetical equation

Next, let's use the hypothetical equation $y = -80 + 0.8x$ to predict the value of $y$ when $x = 177$.

Substitute $x = 177$ into the equation:

$y = -80 + 0.8 \times 177$

Let me calculate that.