The problem presented involves creating scatterplots for two data sets, finding the linear regression equations, and determining which data set is best modeled by a linear regression. Here’s a step-by-step breakdown of what needs to be done:

Part A: Instructions

1. Scatterplot Creation:

   • For each data set, you need to plot the points where:
     • Data Set 1 (x1, y1): (1, 15.38), (2, 12.76), (3, 12.14), (4, 13.12), (5, 13.17), \\ (6, 12.28), (7, 11.86), (8, 8.94), (9, 10.31) \end{aligned}$$
     • Data Set 2 (x2, y2): (1, 21.89), (3, 23.16), (5, 24.14), (7, 24.95), (9, 25.65), \\ (11, 26.27), (13, 26.82), (15, 27.32) \end{aligned}$$
   • These points should be plotted on two separate scatterplots.

2. Finding the Equation of the Linear Regression Line:

   • Once the scatterplots are created, the next step is to find the linear regression equation for both data sets. The general form of a linear equation is $y = mx + b$, where:
     • $m$ is the slope.
     • $b$ is the y-intercept.
   • You will use linear regression formulas or a graphing calculator/software to find these.

3. Determine if a Linear Model is Appropriate:

   • After obtaining the linear regression equations, examine the fit of the linear model by analyzing how well the line fits the scatterplot data. If the points form a roughly straight pattern, a linear model is appropriate. If there is significant curvature or dispersion, it might not be.

Part B: Linear Model Suitability

• You will compare the scatterplots and the linear regression fits from Part A to decide which data set is better modeled by a linear regression. Consider:
  • How closely the data points align with the line.
  • The residuals or differences between the data points and the regression line.

Next Steps

Would you like help with the calculations or visualizing the scatterplots for these data sets?

Relative Questions:

1. What methods can be used to compute the linear regression equation?
2. How can you evaluate the goodness of fit for a linear regression model?
3. What characteristics of data make it suitable for linear modeling?
4. How do residuals help in determining the appropriateness of a linear model?
5. What are common alternatives to linear models if the data does not fit well?

Tip: When performing linear regression, always check for outliers or patterns in residuals that indicate non-linearity.