Explain the transformation needed to convert the following data to a linear data set.
{(1, 0.98), (2, 1.39), (3, 1.71), (4, 1.98), (5, 2.22), (6, 2.43)} (6 points)
To convert the given data set into a linear data set, we need to find a transformation that will make the relationship between the x-values and the y-values linear. One common transformation used for this purpose is taking the logarithm of the y-values.
Here's how we can do it step by step:
1. Start with the given data set: {(1, 0.98), (2, 1.39), (3, 1.71), (4, 1.98), (5, 2.22), (6, 2.43)}.
2. Take the logarithm of the y-values using a base that makes sense for your data. In this case, we can use the natural logarithm (ln) because the values look like they could be exponential.
Applying ln to the y-values, we get:
{(1, ln(0.98)), (2, ln(1.39)), (3, ln(1.71)), (4, ln(1.98)), (5, ln(2.22)), (6, ln(2.43))}.
3. Now we have a transformed data set with a linear relationship between the x-values and the newly calculated y-values.