Beth has been recording her son's weight each year for the past 10 years, as shown in the table below:
Using this table, draw a scatter plot on the graphing calculator DESMOS to determine if the statements below are true or false.
True False
The data suggests a linear association between the recorded age and weight.
True – The data suggests a linear association between the recorded age and weight.
False – The data suggests a linear association between the recorded age and weight.
The data can be represented with a line of best fit y=5x+15
True – The data can be represented with a line of best fit y is equal to 5 x plus 15
False – The data can be represented with a line of best fit y is equal to 5 x plus 15
There is no correlation between the recorded age and weight.
True – There is no correlation between the recorded age and weight.
False – There is no correlation between the recorded age and weight.
To determine if the statements are true or false, we need to plot the data in a scatter plot and analyze the trend.
The given data is as follows:
Based on the scatter plot, we can observe a clear positive correlation between age and weight. As age increases, weight tends to increase as well. Therefore, we can conclude that the statement "The data suggests a linear association between the recorded age and weight" is true.
Next, let's check if the data can be represented with a line of best fit y=5x+15. From the scatter plot, it can be seen that a linear equation with a positive slope (represented by a straight line) does not accurately fit the data points. Therefore, the statement "The data can be represented with a line of best fit y=5x+15" is false.
Lastly, since there is a clear positive correlation between age and weight, we can conclude that there is a correlation between the recorded age and weight. Therefore, the statement "There is no correlation between the recorded age and weight" is false.
In summary:
True - The data suggests a linear association between the recorded age and weight.
False - The data can be represented with a line of best fit y=5x+15.
False - There is no correlation between the recorded age and weight.
To determine if the statements are true or false, we need to first create a scatter plot using the given data.
The table shows the recorded age and weight for Beth's son over the past 10 years.
The age is given as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and the corresponding weights are 20, 25, 30, 35, 40, 45, 50, 55, 60, 65.
To create a scatter plot on DESMOS, follow these steps:
1. Open the DESMOS graphing calculator website (www.desmos.com/calculator).
2. In the input box at the top, type "x" and press Enter.
3. In the next input box, type "y" and press Enter.
4. In the third input box, type "1 20" (age 1 and weight 20) and press Enter.
5. Repeat step 4 for each pair of age and weight data. Each pair should be entered as "age weight" with a space in between.
6. After entering all the data, the scatter plot will be automatically generated on the graphing calculator.
Now we can analyze the scatter plot to determine the truth of the statements:
1. The data suggests a linear association between the recorded age and weight.
To determine if a linear association exists, we need to examine if the points on the scatter plot roughly form a straight line. If they do, the statement is true. If they do not, the statement is false.
2. The data can be represented with a line of best fit y=5x+15.
To determine if the line of best fit equation y=5x+15 accurately represents the data, we need to see if the line passes close to most of the points on the scatter plot. If it does, the statement is true. If it does not, the statement is false.
3. There is no correlation between the recorded age and weight.
To determine if there is no correlation, we need to examine if the points on the scatter plot are randomly scattered and do not follow any particular pattern. If they appear to be randomly scattered, the statement is true. If they exhibit a pattern or trend, the statement is false.
By analyzing the scatter plot, you can answer whether the given statements are true or false based on the visual representation of the data.
To determine if the statements are true or false, we need to plot the data as a scatter plot on a graphing calculator like Desmos. Here are the steps to do so:
1. Go to the website desmos.com or download the Desmos app on your device.
2. Once on the Desmos homepage, click on the "Start Graphing" button.
3. In the input bar at the top left of the screen, enter the data points for the recorded age and weight. For example, if the data points are (1, 10), (2, 15), (3, 20), and so on, you would enter it as (1,10), (2,15), (3,20), and so on.
4. After entering the data points, Desmos will automatically plot the scatter plot on the graphing calculator.
5. Look at the scatter plot and analyze the data points' distribution.
To determine if the data suggests a linear association between the recorded age and weight, you would need to look for a trend in the data points. If the points are roughly arranged in a straight line, there is a linear association. If not, there is no linear association.
To determine if the data can be represented with a line of best fit y=5x+15, you would need to draw a line on the scatter plot that roughly matches the data points' distribution. If the line passes through or is close to most of the data points, this statement is true.
To determine if there is no correlation between the recorded age and weight, you would need to look for any noticeable pattern or trend in the scatter plot. If the data points appear to be randomly scattered, with no clear pattern or trend, then there is no correlation. If there is a pattern or trend (linear or otherwise) in the data points, there is some correlation.
By following these steps and analyzing the scatter plot on the graphing calculator, you can determine the accuracy of the statements provided.