Based on the data shown below, calculate the regression line (each value to at least two decimal places) y = 17.96 19.25 6 22.14 7 26.73 8 26.42 29.71
Based on the data shown below, calculate the regression line (each value to at least two decimal places) y = 17.96 19.25 6 22.14 7 26.73 8 26.42 29.71
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Linear Regression Calculation**
Based on the data shown below, calculate the regression line (each value to at least two decimal places):
\[ y = mx + b \]
| x | y |
|---|------|
| 4 | 17.96|
| 5 | 19.25|
| 6 | 22.14|
| 7 | 26.73|
| 8 | 26.42|
| 9 | 29.71|
**Instructions:**
1. Calculate the slope (\(m\)) using the formula:
\[
m = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{n(\Sigma x^2) - (\Sigma x)^2}
\]
2. Calculate the y-intercept (\(b\)) using the formula:
\[
b = \frac{\Sigma y - m(\Sigma x)}{n}
\]
3. Substitute \(m\) and \(b\) into the linear equation \(y = mx + b\).
*Note: Ensure calculations are accurate to at least two decimal places.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7d5bf39-439e-4459-9b20-3ea6c61a83bb%2F1cf1b941-150e-49c3-9803-416409d7a4c9%2F4effkhl_processed.png&w=3840&q=75)
Transcribed Image Text:**Linear Regression Calculation**
Based on the data shown below, calculate the regression line (each value to at least two decimal places):
\[ y = mx + b \]
| x | y |
|---|------|
| 4 | 17.96|
| 5 | 19.25|
| 6 | 22.14|
| 7 | 26.73|
| 8 | 26.42|
| 9 | 29.71|
**Instructions:**
1. Calculate the slope (\(m\)) using the formula:
\[
m = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{n(\Sigma x^2) - (\Sigma x)^2}
\]
2. Calculate the y-intercept (\(b\)) using the formula:
\[
b = \frac{\Sigma y - m(\Sigma x)}{n}
\]
3. Substitute \(m\) and \(b\) into the linear equation \(y = mx + b\).
*Note: Ensure calculations are accurate to at least two decimal places.*
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