Consider the following. X y 1 2 2 6 (a) Find an equation of the least-squares line for the data. (Round your numerical values to one decimal place.) 15 3 10 y = X Check the degree of your polynomial. 10 4 10 (b) Draw a scatter diagram for the data and graph the least-squares line. y y 5 4 6 15 10 5 2 6 X
Consider the following. X y 1 2 2 6 (a) Find an equation of the least-squares line for the data. (Round your numerical values to one decimal place.) 15 3 10 y = X Check the degree of your polynomial. 10 4 10 (b) Draw a scatter diagram for the data and graph the least-squares line. y y 5 4 6 15 10 5 2 6 X
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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Transcribed Image Text:The image contains four scatter plots, each displaying a set of data points and a line representing a trend or fit. Below is a detailed description of each plot:
### Top Left Plot (Plot a)
- **Axes:** The x-axis ranges from 0 to 6, and the y-axis ranges from 0 to 15.
- **Data Points:** There are four black data points scattered across the plot.
- **Line:** A blue line that is steeply ascending, suggesting a strong positive linear relationship between the variables.
### Top Right Plot (Plot b)
- **Axes:** The x-axis ranges from 0 to 6, and the y-axis ranges from 0 to 15.
- **Data Points:** Four black data points are distributed across the plot.
- **Line:** A blue curved line indicating a potential exponential relationship, with the curve rising steeply as x increases.
### Bottom Left Plot (Plot c)
- **Axes:** The x-axis ranges from 0 to 6, and the y-axis ranges from 0 to 15.
- **Data Points:** Four black data points are scattered.
- **Line:** A blue line with a positive slope, indicating a moderate positive linear relationship.
### Bottom Right Plot (Plot d)
- **Axes:** The x-axis ranges from 0 to 6, and the y-axis ranges from 0 to 15.
- **Data Points:** Four black data points are distributed.
- **Line:** A blue line with a gentle slope, suggesting a weak positive linear relationship.
Each plot illustrates different types of relationships (linear and possibly exponential) between the x and y variables, useful for understanding data trends.
![**Consider the following:**
| \( x \) | 1 | 2 | 3 | 4 |
|-----|---|---|---|---|
| \( y \) | 2 | 6 | 10 | 10 |
(a) **Find an equation of the least-squares line for the data. (Round your numerical values to one decimal place.)**
\( y = \) [ ]
*Check the degree of your polynomial.*
[Red "X" indicating an error in the polynomial degree]
(b) **Draw a scatter diagram for the data and graph the least-squares line.**
**Graph Analysis:**
- **Scatter Diagram (Left Graph):**
- Displays a scatter plot with points at coordinates (1, 2), (2, 6), (3, 10), and (4, 10).
- A blue line represents the least-squares line, which shows a positive linear trend but does not perfectly fit the points.
- **Alternative Graph (Right Graph):**
- Shows a different fitting curve, possibly a higher-degree polynomial, which better approximates the scatter data.
- The blue curve passes closer to more points, suggesting a better fit than the linear line for this dataset.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46a40285-65eb-4b1b-a37e-7e1e7d8c6f08%2F1d1b1e68-807c-4a3a-8808-69a232c51a98%2F1xrtjnt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Consider the following:**
| \( x \) | 1 | 2 | 3 | 4 |
|-----|---|---|---|---|
| \( y \) | 2 | 6 | 10 | 10 |
(a) **Find an equation of the least-squares line for the data. (Round your numerical values to one decimal place.)**
\( y = \) [ ]
*Check the degree of your polynomial.*
[Red "X" indicating an error in the polynomial degree]
(b) **Draw a scatter diagram for the data and graph the least-squares line.**
**Graph Analysis:**
- **Scatter Diagram (Left Graph):**
- Displays a scatter plot with points at coordinates (1, 2), (2, 6), (3, 10), and (4, 10).
- A blue line represents the least-squares line, which shows a positive linear trend but does not perfectly fit the points.
- **Alternative Graph (Right Graph):**
- Shows a different fitting curve, possibly a higher-degree polynomial, which better approximates the scatter data.
- The blue curve passes closer to more points, suggesting a better fit than the linear line for this dataset.
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