Beth has been recording her son's weight each year for the past 10 years, as shown in the table
Age (years) Weight (pounds)
1 - 21
2 - 28
3 - 31
4 - 35
5 - 40
6 - 46
7 - 51
8 - 57
9 - 64
10 - 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)
A. The data can be represented with a line of best fit y = 5x + 15 . True or false?
B. The data suggests a linear association between the recorded age and weight. True or false?
C. There is no correlation between the recorded age and weight. True or false?
To use the graphing calculator DESMOS, follow these steps:
1. Go to the DESMOS website (www.desmos.com) or use their app.
2. Select "Start Graphing."
3. Enter the data from the table as ordered pairs into the calculator. You need to type each pair like `(1, 21)`, `(2, 28)`, and so on until all the pairs are entered.
4. Look at the resulting scatter plot to get a visual representation of the relationship between age and weight.
Based on the data provided in the question, even without using DESMOS, we can make some educated assessments regarding the provided statements:
A. We can't say for sure without actually plotting the points and observing the line of best fit. However, since the line of best fit formula is supposed to predict weight (y) based on age (x), you can try testing a few values to see if it makes sense.
If x = 1 (age 1), y should be 5(1) + 15 = 20, which is close to the actual weight of 21 pounds.
If x = 10 (age 10), y should be 5(10) + 15 = 65, which is close to the actual weight of 71 pounds.
Checking a couple more values from your dataset should give us an idea of how accurate this line of best fit is:
If x = 5 (age 5), y should be 5(5) + 15 = 40, which matches the actual weight.
If x = 8 (age 8), y should be 5(8) + 15 = 55, which is close to the actual weight of 57 pounds.
Based on this quick test, it seems like the line y = 5x + 15 is a reasonable approximation for the dataset, suggesting that statement A is likely to be true.
B. The data suggests a positive association between the recorded age and weight because as the age increases, so does the weight. To confirm if it's linear, you would need to plot the points and observe if they align closely with a straight line. However, looking at the data, the increase in weight is somewhat consistent as age progresses. This makes it reasonable to conclude that there is a linear association, suggesting that statement B is true.
C. There is, in fact, a correlation between the recorded age and weight because as the age increases, the weight also increases. The correlation seems positive and, based on the earlier assessment, linear as well. Thus, statement C is false.
Remember, to make precise conclusions, you should plot the points and the suggested line of best fit y = 5x + 15 on DESMOS or any other graphing calculator to see how well they align.