Question

Beth has been recording her son's weight each year for the past 10 years, as shown in the table below:

Age (years): 1,2,3,4,5,6,7,8,9,10
Weight (pounds): 21, 28,31,35,40,46,51,57,64,71


Using this table, draw a scatter plot on the graphing calculator DESMOS to determine if the statements below are true or false.

(3 points)
True False
The data can be represented with a line of best fit y=5x+15


There is no correlation between the recorded age and weight.


The data suggests a linear association between the recorded age and weight.

Answer 1

To assess the statements regarding Beth's son's weight over the years, we can analyze the data as follows:

1. **Scatter Plot**: You can input the data into Desmos to create a scatter plot. The points are:
- (1, 21)
- (2, 28)
- (3, 31)
- (4, 35)
- (5, 40)
- (6, 46)
- (7, 51)
- (8, 57)
- (9, 64)
- (10, 71)

2. **Line of Best Fit**: To determine if the line of best fit (y = 5x + 15) adequately represents the data, you can check the fit visually on the scatter plot or calculate the correlation coefficient. For a line of best fit to be accurate, it should closely follow the trend of the data points.

3. **Correlation**: The correlation between age and weight appears to be positive, meaning that as age increases, weight also increases. A strong positive correlation indicates a linear relationship.

4. **Analysis of Statements**:
- **"The data can be represented with a line of best fit y=5x+15."**:
- **False**. The slope seems inconsistent with the actual data. You can check this by observing that the weight does not consistently increase by 5 pounds for each additional year. The increase in weight appears to be larger as age increases.

- **"There is no correlation between the recorded age and weight."**:
- **False**. There is a clear positive correlation based on the observed data, as weight increases with age.

- **"The data suggests a linear association between the recorded age and weight."**:
- **True**. The scatter plot will show a linear trend, indicating a strong association between age and weight.

In summary:
- The first statement is **False**.
- The second statement is **False**.
- The third statement is **True**.