x y

Question

−5
3
−4
4
−3
7
−2
7.5
−1
2.5
Use a spreadsheet calculator to determine the least squares regression line for the points in the table. Round to the nearest hundredth if necessary.

(1 point)
Responses

y=5.55x+0.25
y equals 5.55 x plus 0.25

y=0.25x−5.55
y equals 0.25 x minus 5.55

y=5.55x−0.25
y equals 5.55 x minus 0.25

y=0.25x+5.55

Answer 1

To determine the least squares regression line, we need to calculate the slope (m) and y-intercept (b) of the line represented by the formula \(y = mx + b\).

Given the data points: \[ \begin{align*} x: & \quad -5, -4, -3, -2, -1 \ y: & \quad 3, 4, 7, 7.5, 2.5 \ \end{align*} \]

Using a spreadsheet calculator or statistical software, we can input this data and compute the regression line.

To calculate the regression using the least squares method, the following formulas are typically used:

1. The slope \(m\): \[ m = \frac{N(\sum xy) - (\sum x)(\sum y)}{N(\sum x^2) - (\sum x)^2} \]

2. The y-intercept \(b\): \[ b = \frac{\sum y - m(\sum x)}{N} \]

Where:

• \(N\) is the number of points
• \(\sum\) denotes the summation over all points

After performing these calculations (or using a spreadsheet), you should find that the least squares regression line is:

y = 5.55x + 0.25.

So the correct choice is: y = 5.55x + 0.25.