Question

In two or more complete sentences, describe how to determine the appropriate model for the set of data (1, 1), (3, 2), (6, 3), (11, 4).

a) Identify the independent and dependent variables.
b) Plot the points on a graph and look for a pattern.
c) Choose a mathematical function that best fits the observed trend.
d) Conduct a regression analysis to validate the model.

Answer 1

To determine the appropriate model for the given data, identify the independent and dependent variables, plot the points on a graph, check for a pattern or relationship, and calculate the least-squares line.

Step-by-step explanation:

To determine the appropriate model for the set of data (1, 1), (3, 2), (6, 3), (11, 4), follow these steps:

1. Identify the independent variable, which is the input or x-value, and the dependent variable, which is the output or y-value. In this case, the independent variable is the first number in each pair, and the dependent variable is the second number.
2. Plot the given points on a graph, using the independent variable as the x-axis and the dependent variable as the y-axis.
3. Observe the plotted points and see if there is a clear pattern or relationship between the variables. In this case, there appears to be a linear relationship between the variables, as the points form a straight line.
4. Calculate the least-squares line, also known as the best-fit line, by finding the equation of the line that minimizes the sum of the squared differences between the observed y-values and the predicted y-values. The equation of the least-squares line is in the form y = a + bx, where a is the y-intercept and b is the slope of the line.