Beth has been recording her son’s weight each year for the past 10 years, as shown in the table below.
The table shows age in years from 1 to 10 and the corresponding weight in pounds as 21, 28, 31, 35, 40, 46, 51, 57, 64, 71.
Using this table, determine if the statements below are true or false.
There is no correlation between the recorded age and weight.
The data can be represented with a line of best fit of y =5x+15
.
The data suggest a linear association between the recorded age and weight.
False. The data suggest a linear association between the recorded age and weight.
False. The data cannot be represented with a line of best fit of y =5x+15.
True. The data suggest a linear association between the recorded age and weight.
To determine if the statements are true or false, let's analyze the data.
The table shows the age and weight pairs as:
Age: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Weight: 21, 28, 31, 35, 40, 46, 51, 57, 64, 71
Statement 1: There is no correlation between the recorded age and weight.
To determine if there is a correlation, we can plot the data points on a scatter plot.
Age (x) | Weight (y)
------- | ----------
1 | 21
2 | 28
3 | 31
4 | 35
5 | 40
6 | 46
7 | 51
8 | 57
9 | 64
10 | 71
Plotting the data points on a scatter plot, it is clear that there is a positive correlation between age and weight. So, statement 1 is FALSE.
Statement 2: The data can be represented with a line of best fit of y = 5x + 15.
To determine if this is true, we can plot the line of best fit on the scatter plot.
Plotting the line of best fit y = 5x + 15, it does not appear to fit the data very well. So, statement 2 is FALSE.
Statement 3: The data suggest a linear association between the recorded age and weight.
From the scatter plot, it is evident that there is a linear association between the recorded age and weight. As the age increases, the weight also generally increases. So, statement 3 is TRUE.
In conclusion:
Statement 1 is FALSE.
Statement 2 is FALSE.
Statement 3 is TRUE.