## Math Problem Statement

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

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Linear Regression

Least Squares

Algebra

### Formulas

y = a + bx (equation of a line)

Slope formula: b = Σ((x - x̄)(y - ȳ)) / Σ((x - x̄)^2)

### Theorems

Least Squares Regression

### Suitable Grade Level

Grades 10-12

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