Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.]  Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent?  Part C: Does the data in the table represent correlation or causation? Explain your answer.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] 

Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? 

Part C: Does the data in the table represent correlation or causation? Explain your answer.  

### Time vs Surface Area Data

The following table shows the relationship between time elapsed (in days) and surface area (in square feet).

| **Time (x)**  | 5  | 10  | 15  | 20  |
|---------------|----|-----|-----|-----|
| **Surface Area (y)** | 90 | 85  | 70  | 61  |

#### Explanation

This table displays how the surface area in square feet changes over time measured in days. 

- At day 5, the surface area is 90 square feet.
- At day 10, the surface area decreases to 85 square feet.
- At day 15, it decreases further to 70 square feet.
- By day 20, the surface area is down to 61 square feet.

This data can be useful in understanding trends over time or predicting future values based on the given data points. 

#### Graphical Representation

If we were to plot this data on a graph, the x-axis would represent **Time (days)**, while the y-axis would represent **Surface Area (square feet)**. Each point on the graph would correspond to the pairs of values given in the table.

For example:
- (5, 90) 
- (10, 85)
- (15, 70)
- (20, 61)

These points might be connected with a line to visualize the downward trend in surface area over time.
Transcribed Image Text:### Time vs Surface Area Data The following table shows the relationship between time elapsed (in days) and surface area (in square feet). | **Time (x)** | 5 | 10 | 15 | 20 | |---------------|----|-----|-----|-----| | **Surface Area (y)** | 90 | 85 | 70 | 61 | #### Explanation This table displays how the surface area in square feet changes over time measured in days. - At day 5, the surface area is 90 square feet. - At day 10, the surface area decreases to 85 square feet. - At day 15, it decreases further to 70 square feet. - By day 20, the surface area is down to 61 square feet. This data can be useful in understanding trends over time or predicting future values based on the given data points. #### Graphical Representation If we were to plot this data on a graph, the x-axis would represent **Time (days)**, while the y-axis would represent **Surface Area (square feet)**. Each point on the graph would correspond to the pairs of values given in the table. For example: - (5, 90) - (10, 85) - (15, 70) - (20, 61) These points might be connected with a line to visualize the downward trend in surface area over time.
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