Consider the following data from a sample of n=7.

x 178 176 174 166 172 172 174 

The y-intercept of the least squares line is -99.2105263157895. Compute the slope of the least squares line and enter the equation of the least squares line below. (As always, if you round, make sure you do so correctly, only round your final answer, and keep at least three decimal places.)

The least squares line is y =

Regardless of what answer you actually got, suppose your regression equation were y= -80 + 0.8x.

For x = 177, the hypothetical line predicts the value of y will be 


### 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.

Consider the following data from a sample of n=7.

x 178 176 174 166 172 172 174

The y-intercept of the least squares line is -99.2105263157895. Compute the slope of the least squares line and enter the equation of the least squares line below. (As always, if you round, make sure you do so correctly, only round your final answer, and keep at least three decimal places.)

The least squares line is y =

Regardless of what answer you actually got, suppose your regression equation were y= -80 + 0.8x.

For x = 177, the hypothetical line predicts the value of y will be

Learn how to calculate the least squares line for a given dataset with sample size n=7 and a y-intercept of -99.210526. This problem focuses on linear regression, the least squares method, and slope calculation, with detailed solutions and explanations. Suitable for Grades 10-12.

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