Analyzing Data Over Time - Part 1 Analyzing Data Over Time Part 1, Slide 1Copyright © 2004, Jim Schwab, University of Texas at Austin.

Analyzing Data Over Time - Part 1

Analyzing Data Over Time Part 1, Slide 1 Copyright © 2004, Jim Schwab, University of Texas at Austin

Predicting the Future - 1

An essential part of managing any social agency is planning and preparing for the future. This requires that we make some effort to estimate or forecast the future activities of the agency. This week, we will look at quantitative strategies for forecasting using Excel.

Before proceeding, we should point out that quantitative forecasting is only one type of forecasting and only works for a limited range of problems, such as estimation of population and stable economic indicators. There are many future issues not amenable to quantitative forecasting, most notably the stock market. Non-quantitative forecasting is often based on the collection of knowledgeable experts who have shown success at being correct in the past.

Quantitative forecasting requires that we have some numeric, historical data for the event we want to predict, referred to as a time-series. The forecasting task is to find a trend line that fits or models the historical data, and use that trend line as a basis for predicting the event in the future.


Predicting the Future - 2

There are many more complicated methods for forecasting, such as econometric models which attempt to predict future events based on complex interactions.

In this exercise, we will first forecast the Consumer Price Index or CPI which is used to adjust governmental payments such as social security using a linear trend line.

The second example in this exercise will examine a non-linear trend line for predicting population growth, specifically the growth of the population in Texas.


Navigate to the Bureau of Labor Statistics Home Page

The Consumer Price Index is stored on a web site at the Bureau of Labor Statistics.

Type in the URL for the Consumer Price Indexes Home Page: http://stats.bls.gov.

The Consumer Price Index is stored on a web site at the Bureau of Labor Statistics.

Type in the URL for the Consumer Price Indexes Home Page: http://stats.bls.gov.


Navigate the link for the Consumer Price Index

Click on the link for the Consumer Price Index.

Click on the link for the Consumer Price Index.


Navigate the link for detailed CPI statistics

Click on the link Get Detailed CPI Statistics to go to the web page that enables us to access the data.

Click on the link Get Detailed CPI Statistics to go to the web page that enables us to access the data.


Navigate the link for the CPI statistics (current series)

Click on the link All Urban Consumers (Current Series) on the list of most current series.

Click on the link All Urban Consumers (Current Series) on the list of most current series.


Select the data series: U.S. All Items, 1982-84=100

Mark the check box for U.S. All Items, 1982-84=100, to obtain the data for the CPI indexed to 100 during the time period between 1982 and 1984.

Mark the check box for U.S. All Items, 1982-84=100, to obtain the data for the CPI indexed to 100 during the time period between 1982 and 1984.


Retrieve the desired data

Scroll down the web page until you see the Retrieve data button.

Scroll down the web page until you see the Retrieve data button.

Click on the Retrieve data button.

Click on the Retrieve data button.


The link to specify data request

Click on the link More Formatting Options to specify exactly what data we would like.

Click on the link More Formatting Options to specify exactly what data we would like.


The specifications for the data

First, using the popup menus, change the year range from 1991 to 2003.

First, using the popup menus, change the year range from 1991 to 2003.

Second, select Annual Data as the time period that we want.

Second, select Annual Data as the time period that we want.

We will specify two changes to get the exact data that we want.

We will specify two changes to get the exact data that we want.


The specifications for type of output

Second, we can paste both HTML tables and text tables into Excel. For this exercise we will copy and paste the HTML table, so we accept the default output as an HTML table.

Second, we can paste both HTML tables and text tables into Excel. For this exercise we will copy and paste the HTML table, so we accept the default output as an HTML table.

Third, click on the Retrieve Data button to see the final result.

Third, click on the Retrieve Data button to see the final result.

First, scroll down the page until you see the Retrieve Data button.

First, scroll down the page until you see the Retrieve Data button.


Copy the output to the clipboard

First, scroll down the page until you see the two columns of data: Year and Annual. The annual column contains the annual average CPI index.

First, scroll down the page until you see the two columns of data: Year and Annual. The annual column contains the annual average CPI index.

Second, drag select the two columns of data.

Second, drag select the two columns of data.

Third, select the Copy command from the Edit menu to copy the data to the clipboard.

Third, select the Copy command from the Edit menu to copy the data to the clipboard.


Paste the CPI data into Excel

Open a new Excel workbook.

Open a new Excel workbook.

Click on the Paste tool button on the Standard tool bar.

Click on the Paste tool button on the Standard tool bar.

The CPI data is now available as data in Excel.

The CPI data is now available as data in Excel.


Save the CPI data as an Excel Workbook

To rename the workbook and save it in a directory where we can later find it, we complete the specifications in the Save As dialog box. We will name the workbook CPI.xls and save it as an Excel file on our computer’s hard drive.

To rename the workbook and save it in a directory where we can later find it, we complete the specifications in the Save As dialog box. We will name the workbook CPI.xls and save it as an Excel file on our computer’s hard drive.


Remove the web formatting from the table

To remove the web formatting (colors and fonts) from the cells, select the cells A1 through B14 and choose the Clear > Formats command from the Edit menu.



Delete the entry for 2003 from the table

Clear the value for 2003 from the table. This is the value that we will forecast.

Right click on cell B14 and select Clear Contents from the popup menu.

We note the actual value of 184, which we can compare to our predicted value.



We note the actual value of 184, which we can compare to our predicted value.


Format the table

First, substitute the title CPI for the web header for the CPI data.

Bold and center both column headers.

First, substitute the title CPI for the web header for the CPI data.


Second, format all of the numbers in the CPI column to have 1 decimal place.

Second, format all of the numbers in the CPI column to have 1 decimal place.

Third, put outside borders around cells A1 through B1, cells A1 through A14, and cells B1 through B14.

Third, put outside borders around cells A1 through B1, cells A1 through A14, and cells B1 through B14.


Create chart for CPI by year

First, select the data for the chart, cells A2 through B13.


Second, open the Chart tool bar and select the XY (Scatter) Chart as the type of chart to create.


After the basic scatter chart has been created, close the Chart tool bar.


We will use a line chart to show the average progress for each review period. Though Excel has a chart type called a Line chart, we will use the XY (Scatter) chart.



Position the chart

Move the chart so that its top, left corner is in the upper left corner of cell C1.



Resize the chart

Resize the chart on the worksheet by dragging its handles.



Add lines to connect the data points

The default XY (Scatter) chart does not connect the data points with lines. We will change the chart type to add the lines.

The default XY (Scatter) chart does not connect the data points with lines. We will change the chart type to add the lines.

Right click on the chart area, and select Chart Type from the popup menu.



Make chart scatter with data points connected by lines

In the Chart Type dialog box, click on the thumbnail sketch of a scatter chart with data points connected by lines.


Click on the OK button to change the chart type.



Remove the legend from the chart

To remove the legend from a chart, right click on the legend and select Clear from the popup menu.


We have only one series of data on the chart, so we do not need the legend, which does not really contain any useful information on its own.



Add a title to the chart and to the axes

Right click on the chart and select Chart Options from the popup menu.

Click on the Titles tab.



First, click in the Chart title text box and type Consumer Price Index, 1991-2002 as the chart title. After a slight delay, Excel adds the chart title to the thumbnail sketch of the chart.

First, click in the Chart title text box and type Consumer Price Index, 1991-2002 as the chart title. After a slight delay, Excel adds the chart title to the thumbnail sketch of the chart.

Second, select the Value (X) axis text box and type Year.


Third, select the Value (Y) axis text box and type Consumer Price Index.

Third, select the Value (Y) axis text box and type Consumer Price Index.


Add data labels to the points

To add data labels, double click on one of the points to open the Format Data Series dialog box, and mark the check box for Value on the Data Labels tab.

To add data labels, double click on one of the points to open the Format Data Series dialog box, and mark the check box for Value on the Data Labels tab.


Reduce the size of the title font

Select the chart title and reduce the size of the text to 12 point Bold Arial.



Reduce the size of the title font for the axes

Select the vertical axis title and reduce the size of the text to 10 point Bold Arial.


Select the horizontal axis title and reduce the size of the text to 10 point Bold Arial.



Format the font for the data labels and axes

Format the data labels and the labels on both axes so that they are displayed in 8 point, Arial Bold.

Format the data labels and the labels on both axes so that they are displayed in 8 point, Arial Bold.


Clear the plot area background color and grid lines

Right click on the Plot Area of the bar chart and select Clear from the popup menu. This will clear the gray background color from the plot area.

Right click on a grid line and select Clear from the popup menu. This will clear the grid lines from the plot area.


Right click on a grid line and select Clear from the popup menu. This will clear the grid lines from the plot area.


Position value labels above data points

Double click on one of the data points to open the Format Data Labels dialog box.

Double click on one of the data points to open the Format Data Labels dialog box.

Click on the Alignment tab to navigate to that panel.

Click on the Alignment tab to navigate to that panel.

Select Above on the Label Position drop down list.

Select Above on the Label Position drop down list.

Click on the OK button to re-position the labels.

Click on the OK button to re-position the labels.


The chart with repositioned data labels

The data labels are positioned above the plot line, but are not readable because of the limited chart space.

We will alternate the data labels so that every other one is above and below the line.

The data labels are positioned above the plot line, but are not readable because of the limited chart space.

We will alternate the data labels so that every other one is above and below the line.


Select the second data label in the series

Select the second data label.

Click once on the label to select all data labels. Click a second time on the second data label to select it individually.

Select the second data label.

Click once on the label to select all data labels. Click a second time on the second data label to select it individually.


Change the label position to below the line

With the second label selected, right click on it and select Format Data Labels from the popup menu, and select the Alignment tab in the Format Data Labels dialog box.

With the second label selected, right click on it and select Format Data Labels from the popup menu, and select the Alignment tab in the Format Data Labels dialog box.

Change the Label Position from Above to Below.

Change the Label Position from Above to Below.

Click on the OK button to apply the change.

Click on the OK button to apply the change.


The chart with the second data label below the line

The second data label is now positioned below the line.

Repeat these steps for the fourth, sixth, eighth, tenth, and twelfth data labels.

The second data label is now positioned below the line.

Repeat these steps for the fourth, sixth, eighth, tenth, and twelfth data labels.


The chart with data labels above and below the line

When we are finished, the label for every other point is above or below the line.

When we are finished, the label for every other point is above or below the line.


Add a trendline to the chart

Right click on one of the data points and select Add Trendline from the popup menu.



Complete the add trendline dialog box

First, the default Linear trendline is the one we want to add to the chart, so we accept the default.

First, the default Linear trendline is the one we want to add to the chart, so we accept the default.

Second, we click on the OK button.



The trend line on the line chart

The trend line is drawn as a straight black line through the middle of the data points, obscuring the line connecting the data points.

In this chart, the trend line is not really obvious, so we will change its color.

The trend line is drawn as a straight black line through the middle of the data points, obscuring the line connecting the data points.

In this chart, the trend line is not really obvious, so we will change its color.

First, double click on the trend line to open the Format Trendline dialog box.

First, double click on the trend line to open the Format Trendline dialog box.


Change the color of the trendline

First, click on the Patterns tab where color selection is located.


Second, click on the Color drop down palette.

Second, click on the Color drop down palette.

Third, click on the Bright Green color swatch (fourth row, fourth from left).

Third, click on the Bright Green color swatch (fourth row, fourth from left).

Fourth, click on the OK button to apply the color.

Fourth, click on the OK button to apply the color.


The line chart with a trend line

The linear trend line fits the pattern of the data very closely. We can use a linear trend to compute the forecast of the CPI for 2003.

The linear trend line fits the pattern of the data very closely. We can use a linear trend to compute the forecast of the CPI for 2003.


Forecasting the CPI for 2003

We will use Excel's function wizard to create the FORECAST function.

We will use Excel's function wizard to create the FORECAST function.

First, select cell B14 as the destination where we will store the result of the FORECAST function.

First, select cell B14 as the destination where we will store the result of the FORECAST function.

Second, select the Function command from the Insert menu.



Locate the forecast function by searching

We will search for the FORECAST function.

We will search for the FORECAST function.

The FORECAST function name will appear in the Select a function list box.

The FORECAST function name will appear in the Select a function list box.

Click on the OK button access the dialog box where the function arguments are entered.


First, type FORECAST in the Search for a function text box.

First, type FORECAST in the Search for a function text box.

Second, click on the Go button.



The arguments to the forecast function - 1

The second argument to the FORECAST function is the Known_y's, which are the known CPI figures, in cells B2 through B13.

The second argument to the FORECAST function is the Known_y's, which are the known CPI figures, in cells B2 through B13.

The first argument to the FORECAST function is the X, or year for which we want to estimate the CPI. The year for which we want a forecast is 2003, in cell A14.

The first argument to the FORECAST function is the X, or year for which we want to estimate the CPI. The year for which we want a forecast is 2003, in cell A14.


The arguments to the forecast function - 2

The third argument to the FORECAST function is the Known_x's, which are the years for which we have known CPI figures, in cells A2 through A13.

The third argument to the FORECAST function is the Known_x's, which are the years for which we have known CPI figures, in cells A2 through A13.

Click on the OK button to compute the function.



The forecast for CPI for 2003

The forecast for 2003 using a linear trend method is approximately 183.9.

A forecast of 183.9 compares favorably to the actual value for 2003 of 184.0, indicating that the linear forecast matches the data well.

The forecast for 2003 using a linear trend method is approximately 183.9.

A forecast of 183.9 compares favorably to the actual value for 2003 of 184.0, indicating that the linear forecast matches the data well.


Add a discussion text box at the base of the chart

To add a discussion text box for the line chart, click on the Text Box tool button and click an insertion point at the base of the chart. Type the text in the text box: Based on a linear relationship between Year and CPI, the estimated CPI for 2003 is 183.9.

To add a discussion text box for the line chart, click on the Text Box tool button and click an insertion point at the base of the chart. Type the text in the text box: Based on a linear relationship between Year and CPI, the estimated CPI for 2003 is 183.9.

The chart for the forecasting the with a linear trend is now complete.

The chart for the forecasting the with a linear trend is now complete.


Forecasting a non-linear time series

Forecasting with a linear trend line is not always the best model for predicting the future. For example, the growth in a population may not follow a linear pattern. As a population grows, the rate of change is often increasing as new generations produce their own children. In addition, a country or state may experience a steady inflow of immigrants or new citizens who accelerate the change in population.

The pattern in population growth may fit what Excel refers to as a growth curve, i.e. the rate of change from year to year increases over time. This is characteristic of the population growth in Texas, and many other areas of the south, where in-migration has added to the increase in the native population. In this situation, an exponential curve may provide a better tool for forecasting future estimates.

We use data for the Texas population found at a web site created by the Texas State Libraries and Archives Commission to chart Texas population growth over time. We will compare the results we would obtain with a forecast based on a linear trend line to a forecast based on an exponential trend line.


Web site with Texas population data

Navigate to the Texas State Libraries and Archives Commission web page that lists US and Texas populations by typing in the URL as shown in the address box.

Navigate to the Texas State Libraries and Archives Commission web page that lists US and Texas populations by typing in the URL as shown in the address box.


Locate Official U.S. Census Count and Estimate

First, scroll down the web page to locate the table for the Official U.S. Census Count and Estimate.

First, scroll down the web page to locate the table for the Official U.S. Census Count and Estimate.

Second, select all of the text in the population table.

Second, select all of the text in the population table.

Third, select the Copy command from the Edit menu.

Third, select the Copy command from the Edit menu.


Paste the clipboard into the worksheet

We want to copy the data table on the clipboard to our Excel worksheet.

We want to copy the data table on the clipboard to our Excel worksheet.

First, select cell A1 in a new workbook as the destination for the table.

First, select cell A1 in a new workbook as the destination for the table.

Second, click on the Paste tool button. The table is pasted into the worksheet.

Second, click on the Paste tool button. The table is pasted into the worksheet.


Save the data as an Excel Workbook

To rename the workbook and save it in a directory where we can later find it, we complete the specifications in the Save As dialog box.

We will name the workbook TexasPopulation.xls and save it as an Excel file on our computer’s hard drive.

To rename the workbook and save it in a directory where we can later find it, we complete the specifications in the Save As dialog box.

We will name the workbook TexasPopulation.xls and save it as an Excel file on our computer’s hard drive.


Replace data missing in D and E

There are two time periods, 1970 on row 79 and 1980 on row 89, in which the table entries for columns D and E are missing. We will replace these missing entries with the data in columns B and C.

There are two time periods, 1970 on row 79 and 1980 on row 89, in which the table entries for columns D and E are missing. We will replace these missing entries with the data in columns B and C. First, scroll down to

the cells missing data in columns D and E, e.g. row 79.

First, scroll down to the cells missing data in columns D and E, e.g. row 79.

Second, copy the data in cells B79 and C79 and paste it into cells D79 and E79.

Second, copy the data in cells B79 and C79 and paste it into cells D79 and E79.

Third, copy the data in cells B89 and C89 and paste it into cells D89 and E89.

Third, copy the data in cells B89 and C89 and paste it into cells D89 and E89.


Delete extraneous columns B, C, and E

We do not need the data in columns B, C, and E, so we delete them from the worksheet, leaving only the Year column and the Texas Census column.

We do not need the data in columns B, C, and E, so we delete them from the worksheet, leaving only the Year column and the Texas Census column.


Delete extraneous rows 1-2 and 4-8 from worksheet

Some of the rows, 1 through 2 and 4 through 8, are not needed for this exercise, so they are deleted.

Some of the rows, 1 through 2 and 4 through 8, are not needed for this exercise, so they are deleted.


Remove the web formatting from the table




Format the population data

First, select the cells with the population data: B2 through B105.

First, select the cells with the population data: B2 through B105.

Second, click on the Comma Style tool button to add comma separators to the population numbers.

Second, click on the Comma Style tool button to add comma separators to the population numbers.

Third, click on the Decrease Decimal tool button twice to eliminate the decimal and trailing zeros added by the comma formatting.

Third, click on the Decrease Decimal tool button twice to eliminate the decimal and trailing zeros added by the comma formatting.


Format the table

First, substitute the title Year for the web header for the YEAR data.


First, substitute the title Year for the web header for the YEAR data.


Second, put outside borders around cells A1 through B1, cells A1 through A105, and cells B1 through B105.

Second, put outside borders around cells A1 through B1, cells A1 through A105, and cells B1 through B105.


Delete the entry for 2003 from the table



We note the actual value of 22,118,509, which we can compare to our predicted value.



We note the actual value of 22,118,509, which we can compare to our predicted value.


Create chart for population by year










Position the chart




Resize the chart




Add lines to connect the data points

The default XY (Scatter) chart does not connect the data points with lines. We will change the chart type to add the lines, even though there are so many data points that they appear to follow a line.

The default XY (Scatter) chart does not connect the data points with lines. We will change the chart type to add the lines, even though there are so many data points that they appear to follow a line.




Make chart scatter with data points connected by lines






Remove the legend from the chart






Add a title to the chart and to the axes





First, click in the Chart title text box and type Texas Population, 1900-2002 as the chart title. After a slight delay, Excel adds the chart title to the thumbnail sketch of the chart.

First, click in the Chart title text box and type Texas Population, 1900-2002 as the chart title. After a slight delay, Excel adds the chart title to the thumbnail sketch of the chart.



Third, select the Value (Y) axis text box and type Population.

Third, select the Value (Y) axis text box and type Population.


Reduce the size of the title font




Reduce the size of the title font for the axes






Format the font for the axes labels

Format the labels on both axes so that they are displayed in 8 point, Arial Bold.

Format the labels on both axes so that they are displayed in 8 point, Arial Bold.


Clear the plot area background color



We will not remove the grid lines. With so many data points, we cannot use data labels, so the only means we have for estimating values for any given year is supported by the grid lines.

We will not remove the grid lines. With so many data points, we cannot use data labels, so the only means we have for estimating values for any given year is supported by the grid lines.


Add a trend line to the chart




Complete the add trend line dialog box

First, the default Linear trend line is the one we want to add to the chart, so we accept the default.

First, the default Linear trend line is the one we want to add to the chart, so we accept the default.




The trend line on the line chart

The trend line is drawn as a straight black line through the middle of the data points. Because the actual population data fits more of a curved pattern, using the trend line to forecast future population would result in our underestimating the future population

The trend line is drawn as a straight black line through the middle of the data points. Because the actual population data fits more of a curved pattern, using the trend line to forecast future population would result in our underestimating the future population

Moreover, the farther we try to estimate in the future, the larger will be the underestimate.

Moreover, the farther we try to estimate in the future, the larger will be the underestimate.


Change the type of the trend line

We will try another type of trend line to see if we can obtain a pattern that better fits the historical data.

We will try another type of trend line to see if we can obtain a pattern that better fits the historical data.

Double click on the trend line to open the Format Trendline dialog box.

Double click on the trend line to open the Format Trendline dialog box.


Select the exponential trend line

First, click on the Type tab in the Format Trendline dialog box.

First, click on the Type tab in the Format Trendline dialog box.

The thumbnail sketched for the Power and the Exponential trend lines are more similar to the shape of the curve on our population chart.

We will use the exponential function because it is commonly used to represent increases in populations which grow at an increasing rate over time.

The thumbnail sketched for the Power and the Exponential trend lines are more similar to the shape of the curve on our population chart.

We will use the exponential function because it is commonly used to represent increases in populations which grow at an increasing rate over time.

While the Format Trendline dialog box is available, we will change the appearance of the trend line after changing its type.

While the Format Trendline dialog box is available, we will change the appearance of the trend line after changing its type.


Change the color and weight of the trend line



Second, click on the Color drop down palette and select the Red color swatch.

Second, click on the Color drop down palette and select the Red color swatch.

Third, click on the Weight drop down arrow and select the thickest line available, the last one in the list.

Third, click on the Weight drop down arrow and select the thickest line available, the last one in the list.

Fourth, click on the OK button to change the trend line.

Fourth, click on the OK button to change the trend line.


The line chart with an exponential trend line

The red exponential trend line fits the pattern of the population data points much more closely than did the linear trend line. We would expect our estimate for future population to be much more accurate based on this trend line.

The red exponential trend line fits the pattern of the population data points much more closely than did the linear trend line. We would expect our estimate for future population to be much more accurate based on this trend line.

The Excel function which calculates the numeric forecast corresponding to an exponential trend line is the GROWTH function.

The Excel function which calculates the numeric forecast corresponding to an exponential trend line is the GROWTH function.


Forecasting Texas Population for 2003

We will use Excel's function wizard to create the GROWTH function.

We will use Excel's function wizard to create the GROWTH function.

First, select cell B105 as the destination where we will store the result of the GROWTH function.

First, select cell B105 as the destination where we will store the result of the GROWTH function.




Locate the growth function by searching

We will search for the GROWTH function.

We will search for the GROWTH function.

The GROWTH function name will appear in the Select a function list box.

The GROWTH function name will appear in the Select a function list box.



First, type GROWTH in the Search for a function text box.

First, type GROWTH in the Search for a function text box.




The arguments to the growth function - 1

The first argument to the GROWTH function is the Known_y's, which are the known population figures, in cells B2 through B104.

The first argument to the GROWTH function is the Known_y's, which are the known population figures, in cells B2 through B104.

The second argument to the GROWTH function is the Known_x's, which are years for which we have known population figures, in cells A2 through A104.

The second argument to the GROWTH function is the Known_x's, which are years for which we have known population figures, in cells A2 through A104.


The arguments to the growth function - 2

The third argument to the GROWTH function is the New_x's, or year for which we want to estimate the population. The year for which we want a forecast is 2003, in cell A105.

The third argument to the GROWTH function is the New_x's, or year for which we want to estimate the population. The year for which we want a forecast is 2003, in cell A105.

The final argument to the GROWTH function is a true/false value that tells Excel how to calculate the function. We use TRUE to do the normal calculation of the constant in the equation.

The final argument to the GROWTH function is a true/false value that tells Excel how to calculate the function. We use TRUE to do the normal calculation of the constant in the equation.




The forecast for Texas population for 2003

The forecast for 2003 using an exponential trend method is approximately 21,532,216 people.

A forecast of 21,532,216 is an underestimate of 2.7% of the actual value for 2003 of 22,118,509, indicating that the exponential forecast matches the data reasonably well, certainly more accurately than an estimate based on a linear trend line.

The forecast for 2003 using an exponential trend method is approximately 21,532,216 people.

A forecast of 21,532,216 is an underestimate of 2.7% of the actual value for 2003 of 22,118,509, indicating that the exponential forecast matches the data reasonably well, certainly more accurately than an estimate based on a linear trend line.


Add a discussion text box at the base of the chart

To add a discussion text box for the line chart, click on the Text Box tool button and click an insertion point at the base of the chart. Type the text in the text box: An exponential function was used with data from the years 1900 to 2002 to forecast that the Texas population in 2003 would be 21,532,216 people.

To add a discussion text box for the line chart, click on the Text Box tool button and click an insertion point at the base of the chart. Type the text in the text box: An exponential function was used with data from the years 1900 to 2002 to forecast that the Texas population in 2003 would be 21,532,216 people.

The chart for forecasting the with an exponential trend is now complete.

The chart for forecasting the with an exponential trend is now complete.


Analyzing Data Over Time - Part 1 Analyzing Data Over Time Part 1, Slide 1Copyright © 2004, Jim Schwab, University of Texas at Austin.

Documents

data series

university of texas

jim schwab

historical data

time period

type of forecasting

nonquantitative forecasting

forecasting task