Because of high tuition costs at state and private...

Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands) for Jefferson Community College from $2001-2009$. $$\begin{array}{ccc}\text { Year } & \text { Period }(t) & \text { Enrollment }(1000 \mathrm{s}) \\2001 & 1 & 6.5 \\2002 & 2 & 8.1 \\ 2003 & 3 & 8.4 \\2004 & 4 & 10.2 \\2005 & 5 & 12.5 \\2006 & 6 & 13.3 \\ 2007 & 7 & 13.7 \\2008 & 8 & 17.2 \\2009 & 9 & 18.1\end{array}$$ a. Construct a time series plot. What type of pattern exists in the data? b. Develop the linear trend equation for this time series. c. What is the forecast for $2010 ?$

Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands) for Jefferson Community College from $2001-2009$.
$$\begin{array}{ccc}\text { Year } & \text { Period }(t) & \text { Enrollment }(1000 \mathrm{s}) \\2001 & 1 & 6.5 \\2002 & 2 & 8.1 \\
2003 & 3 & 8.4 \\2004 & 4 & 10.2 \\2005 & 5 & 12.5 \\2006 & 6 & 13.3 \\
2007 & 7 & 13.7 \\2008 & 8 & 17.2 \\2009 & 9 & 18.1\end{array}$$
a. Construct a time series plot. What type of pattern exists in the data?
b. Develop the linear trend equation for this time series.
c. What is the forecast for $2010 ?$

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Key Concepts

Time Series Plot

A time series plot is a graphical representation of data points in time order. It is used to visualize trends, patterns, seasonal effects, and other variations over time, which aids in understanding the behavior of the data and in identifying underlying patterns like trends or cycles.

Trend Analysis

Trend analysis involves examining time series data to determine whether the underlying pattern is increasing, decreasing, or stable over time. It helps in understanding the long-term direction of the data, which is essential in many fields such as economics, finance, and education for making informed projections.

Linear Regression

Linear regression in the context of time series is used to model the relationship between time (independent variable) and the observed data (dependent variable) by fitting a straight line through the data points. This line, obtained by methods like least squares, represents the trend in the data and provides a simple way to understand and quantify that trend.

Forecasting

Forecasting using the linear trend equation involves applying the regression model to predict future values by extrapolating the established relationship between time and the data. This is particularly useful when future estimates are needed, as it relies on the assumption that the identified trend will continue into the future.

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