Question

Identify a time dependent variable in your organization, business, or industry. Collect several measurements of this variable over time. Draw a scatter diagram of this variable versus time. What are your observations?

1. Do you see any trend in the measurements? Explain.

1. Do you see any seasonal variation in the measurements? Explain.

1. Add a trend line to your scatter diagram, and determine the trend equation. Interpret the trend equation.

Purpose:  To demonstrate the application of time series analysis in your organization, business, or industry.

Example:  I work for an electric utility company. Over the years the demand for electricity has been growing constantly. The electricity demand measured in Megawatts is an example of a time dependent variable. When I plot the scatter diagram of electricity demand versus time, I see both an upward trend and seasonal variation. The upward trend is the result of growing demand over time. The electricity demand is high during the summer season, and is low during winter season. This pattern is repeated year after year.

Answer 1

ANSWER:

Given that,

The Constructing a scatter diagram is a fairly straightforward process. First decide which variable is going to be your x-value and which variable is going to be your y-value.

Find the minimum and maximum of your x-values and set up a uniform number line on your horizontal axis so that the values extend from the minimum x-value to the maximum x-value but not much farther.

Next find the minimum and maximum of your y-values and set up a uniform number line on the vertical axis so that the values extend from the minimum y-value to the maximum y-value but not much farther.

Once the axes are set up, you just act like each pair of x- and y-values is an ordered pair, and you plot these ordered pairs on the coordinate axes you just created.

For example, consider Table 1 on page 178 of Sullivan, which is reproduced below. Usually you would pick the first row or column as your x-values and the second row or column as your y-values. Once you make that decision, your axes should be fairly similar to those shown in the figure below.

Club-Head Speed (mph)	100	102	103	101	105	100	99	105
Distance (yards)	257	264	274	266	277	263	258	275

The lowest club head speed is 99 and the highest is 105, and the x-axis shown extends from 99 to 105. The shortest distance is 257 and the largest is 277, but since multiples of 5 were used to mark the scale, the vertical scale extends a little below 257 to 255, and a little above 277 to 280.

Each row of Table 1 on page 178 will be represented by a point on the scatter diagram. To plot the point represented by the first row in the table, you find 100 on the x-axis and then move up to a height representing 257 on the y-axis. Since 257 is between 255 and 260, but closer to 255, that is where the point should be. In a similar fashion, points would be plotted for the other rows in Table 1. Once a point has been plotted for each row and a title has be added to the chart, the scatter diagram is complete.