A Visual Inspection of Your Data, Essay Example

Illustrate what a visual inspection of your data through the use of a scatter plot can help you determine. Summarize the relationship between data points on a scatter plot and a correlation coefficient.

Scatter plots allow the viewer to determine a general data trend. Adding a best fit line to the plot will help determine whether there is a positive correlation between the two variables being examined, if there is a negative correlation, or no correlation. A positive correlation is indicated by a diagonal line that increases as it continues along the x and y axes, a negative correlation is indicated by a diagonal line that decreases as it continues along the x and y axes, and no correlation is represented by either a horizontal or vertical line. While this information is useful to determine the general trend that data follows, it is often important to determine the extent of the positivity or negativity of the correlation. Therefore, it is useful to create a best fit line on the graph and to use this information to determine the correlation coefficient.

The correlation coefficient is also known as the Pearson product-moment correlation coefficient. Calculating the Pearson’s correlation coefficient is helpful because it generates a value between -1 and 1 that allow an individual to determine the extent of the data trend. Since all values are between -1 and 1, the correlation coefficient will be reported as a decimal. Values with a -1 or 1 usually never occur and represent situations in which there is a completely negative relationship between two variables or a completely positive one.

To calculate a correlation coefficient on a plot, Microsoft Excel could be used. To generate the scatter plot, it is essential to first list the x and y variables and their associated data points in a worksheet. Then, a scatter plot should be generated and all axes should be labelled. If the plot does not reflect a numerical scale for the x or y axis that is desirable, it should be adjusted. Next, it is essential to right-click on the data points and select the option that reads “add trend line”. In doing so, Microsoft Excel will allow section of a variety of options for trend line selection, including linear, exponential, log, and others. A linear trend line should be selected in a majority of cases. However, if the data received is not expected to reflect a linear trend, it may be useful to select one of the other options.

It is possible to display the correlation coefficient on the graph, which is available for selection under the trend line options. In some cases, the program will give the coefficient of determination, which is represented by R². In order to determine the Pearson’s correlation coefficient from this value, simply take the square root of the R² value and it will become r. Understanding the connection between R² and r is useful because it will help determine which type of line (ex. linear, exponential, log) is best to use for a particular data set. To do this, have Microsoft Excel calculate an R² for each linear option available. The one that produces an r value closest to -1 or 1 will optimally represent the trend that is being studied. Ultimately, when values are closest to 1, they have a high positive correlation and when values are closes to -1, they have a high negative correlation. Values closest to 0 have no correlation.