9. 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 to a linear data set, we need to transform it by finding a linear relationship between the x-values and y-values.

One common way to do this is by performing a linear regression analysis. Linear regression is a statistical method used to find the best-fitting line that describes the relationship between two variables.

Let's take a step-by-step approach to performing a linear regression analysis:

1. Define the variables:
- Let x represent the independent variable (in this case, the x-values from the given data set).
- Let y represent the dependent variable (in this case, the y-values from the given data set).

2. Calculate the mean:
- Find the mean of the x-values, denoted as x̄ (pronounced "x-bar").
- Find the mean of the y-values, denoted as ȳ (pronounced "y-bar").

3. Calculate the deviations:
- Calculate the deviation of each x-value from the mean (x - x̄).
- Calculate the deviation of each y-value from the mean (y - ȳ).

4. Calculate the sums of products and squares:
- Multiply the deviations of x and y for each data point (Σ[(x - x̄)(y - ȳ)]).
- Square the deviations of x for each data point (Σ[(x - x̄)^2]).

5. Calculate the regression coefficients:
- Calculate the slope of the regression line (b) using the formula:
b = Σ[(x - x̄)(y - ȳ)] / Σ[(x - x̄)^2]
- Calculate the y-intercept of the regression line (a) using the formula:
a = ȳ - b * x̄

6. Write the equation of the regression line:
- Once you have the values of a and b, the equation of the regression line can be written as:
y = a + b * x

Using the given data set {(1, 0.98), (2, 1.39), (3, 1.71), (4, 1.98), (5, 2.22), (6, 2.43)}, you can follow the steps above to perform the linear regression analysis. The resulting equation of the regression line will give you the linear data set that approximates the relationship between the x-values and y-values.