4.4 Scatter Plots and Lines of Fit

Scatter plots are a way to visualize the relationship between two variables. A line of fit, also known as a trend line, is a straight line that represents the relationship between the two variables.

Here are the steps to create a scatter plot and a line of fit:

1. Choose the two variables you want to plot. For example, if you want to plot the relationship between height and weight, height would be on the x-axis and weight would be on the y-axis.

2. Collect data for the two variables. You will need at least two data points for each variable to create a scatter plot.

3. Plot the data points on the graph. Use one axis for each variable and label the axes appropriately. For example, if height is on the x-axis, label it "Height (inches)". If weight is on the y-axis, label it "Weight (pounds)".

4. Look for any patterns or trends in the data points. If there is a clear relationship between the two variables, you can draw a line of fit to represent the trend.

5. To draw the line of fit, choose two data points that are far apart from each other and that follow the trend of the data. Use the slope-intercept form of a line (y = mx + b) to find the equation of the line. Calculate the slope (m) and the y-intercept (b) using these two data points.

6. Once you have the equation of the line, plot the line on the graph. Use a straight edge or ruler to draw a line that passes through the two data points and follows the trend of the data.

7. If the line of fit does not fit the data well, you may need to choose different data points or use a different type of curve to represent the trend.

8. Label the graph with a title that describes the relationship between the two variables and include any necessary units of measurement.

Suppose you want to explore the relationship between the number of hours students study per week and their grades. You collect data from a random sample of 10 students, and here are the results:

To create a scatter plot, we plot the data points on a graph, with hours of study on the x-axis and grades on the y-axis. The resulting scatter plot looks like this:

From the scatter plot, we can see that there is a positive correlation between hours of study and grades. As students study more, their grades tend to improve. To find the line of fit that best represents this relationship, we can use linear regression.

Using a statistical software or a calculator with linear regression capabilities, we can find that the equation of the line of best fit is:

y = 6.76x + 44.28

This means that for every additional hour of study, the predicted grade increases by 6.76 points. We can now add the line of fit to the scatter plot:

The line of fit helps us see the general trend of the data and make predictions about grades based on the number of hours of study. For example, if a student studies for 5 hours per week, we can predict that their grade will be around 79 (using the equation of the line of fit).