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Square Cube Consulting 1

Steamboat Springs School District – Enrollment Forecast Developed by Jim Looney, Square Cubed Consulting, Ltd. 10/29/16

Scope Square Cubed Consulting has been hired to develop a five-year K12 forecast for the Steamboat Springs School District (SSSD). To do this, Square Cubed Consulting analyzed historical enrollment, births, and new school impacts. Then, three different forecasting methods were used to develop a five-year forecast. Square Cubed Consulting also agreed to provide student yields for different residential unit types. Even though the forecasting methods described in this document account for natural residential development, these yields are important for any future developments that fall outside what is considered normal. Outside the norm is a development that significantly increases the number of closed units in one given year, or a large apartment community that adds 100+ units in one year. Square Cubed Consulting also agreed to provide a scatter plot map for each of the schools that report to the Colorado Department of Education. The scatter plot maps are based on the geocoded student addresses that Square Cubed Consulting received in September 2016. Square Cubed will include the scatter plots in the presentation. Key Data Points 1.0 Historical Enrollment: Between 2000 and 2005, the K12 enrollment for SSSD added a total of 32 students. However, in 2001 and 2003 overall enrollment declined for those specific years. Then between 2006 and 2010, the K12 enrollment saw a dramatic uptick adding 254 students. The increase in enrollment continued between 2011 and 2015, when another 283 students were added. For 2016, the K12 enrollment grew by only 10 students from 2015 (Chart 1.1). Chart 1.1: SSSD K12 Enrollment

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The K12 enrollment growth rate has only seen declines in two years since 2000. In 2013, the K12 enrollment nearly set a new growth rate record at 3.5%. Since 2013, the rate has steadily declined over the last three years (Chart 1.2). Chart 1.2: K12 Enrollment Growth Rates

Besides the declining growth rates there is also a plateau moving through SSSD. In Chart 1.3, the bubble is centered on the 2010 2nd grade with enrollment at 201. By 2016, the same bubble is now in 8th grade and has 230 students. In fact, this cohort in 2016 is the single largest grade for any grade any year between 2010 and 2016. Over the next five years this bubble will graduate and leave SSSD. Chart 1.3: 2010 Enrollment by Grade

Chart 1.4: 2016 Enrollment by Grade

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2.0 Births: Birth data is sourced from the Colorado Department of Health and includes all births within the SSSD boundary. All birth counts are moved forward five years to correspond with that year’s kinder count (i.e., children born in 2005 are counted in the 2010 forecast). This is why you will see birth counts for upcoming years. For the rest of this analysis, any mention of birth counts will be for this 5-year cohort, not birth year, unless specifically called out as birth year. This allows us to see the relationship between birth counts and kinder population. Between 2000 and 2020, SSSD has averaged 132 births per year, peaking in 2010. Births stayed at this elevated level over the next five years, leading to a mini baby boom. Then, due to the recession families started having fewer children. This was seen, not just within SSSD, but also the state of Colorado and the U.S. as a whole. Chart 2.1: Birth and Kinder

As you can see in Chart 2.1, the kinder tends to move in conjunction with the birth count. In fact, as expressed as a correlation coefficient, births to kinder has a coefficient

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of 0.90. In mathematics, a coefficient of 1 means there is a positive linear correlation between the two variables. A coefficient of -1 means that the variables have a negative linear correlation, or simply stated, the variables move in opposite directions. A coefficient of 0 means that the variables have no linear correlation. When forecasting kinder enrollment, having a coefficient of 0.90 means that the kinder enrollment should move in the same general direction as the birth counts. It does not mean they have to be an exact 1 to 1 gain or loss. 3.0 New School Impact: A new Montessori program opened in the SSSD boundary in 2016. At build out it is expected to be a K-8 school. For the opening year, there were 28 students in the kinder class. Of the 28, it is estimated that 20 are SSSD students. For the remaining 1st through 5th grades, there are 50 SSSD residing students. For forecasting purposes the 50 students were distributed more heavily in the lower grades. This was done for two reasons. First, in general families like to have a continuity of education. 4th and 5th grade students are less likely to leave for a new school than lower grades. Second, when looking at the Cohort Comparison Rate for 2016 the kinder and 1st grade rates were below 1.0 for the first time in six years. This is most likely due to the opening of the new school. Below is the estimated grade-by-grade breakout for the new program. These numbers will need to be taken into account when looking at each of the forecasting methods. Chart 3.1: Expected SSSD Reside Children Attending Montessori Program

Year Kind. 1st 2nd 3rd 4th 5th 6th 7th 8th Total

2016 20 20 15 10 2 3

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2017 20 20 20 15 10 2 3

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2018 20 20 20 20 15 10 2 3

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2019 20 20 20 20 20 15 10 2 3 130

2020 20 20 20 20 20 20 15 10 2 147

2021 20 20 20 20 20 20 20 15 10 165

2022 20 20 20 20 20 20 20 20 15 175

2023 20 20 20 20 20 20 20 20 20 180

Forecast Methods The goal of any method is not to hit a specific number exactly. When forecasting, time is best spent on identifying the key data points and gaining certainty on how those key data points will impact your forecasting number. Chasing down every minute data point will not make a forecast more accurate. In fact, it is likely to cause issues due to time taken away from the key data points.


The goal of producing a forecast is to ensure that all potential risks have been identified and accounted for. When forecasting, K12 enrollments the major risks are cohort bubbles, declining birth rates, and new school impacts. By properly identifying the impact of such risk, the stakeholders can then make plans to mitigate any risk. There are three main forecasting methods that can be used. Each of these methods has inherent risks and benefits. Regression: The regression method is standard practice in the field of statistics. The method calculates relationship between multiple variables. A classic example is the price of gas and oil production. In this example, the price of gas is the dependent variable. Oil production is the independent variable. How good of a predictor oil production is for gas prices, is defined as the r-squared value. The closer the r-squared value is to 1.0 the better a predictor it is. For enrollment forecasting there are two independent variables and one dependent variable. The two independent variables are Total Population and Student Age Population, ages 5-17 (SAP). The dependent variable is the K12 enrollment. The State Demographers office provided the two independent variables. In my experience, the forecast provided by the state are significantly overstated. At the state level the 10-year Total Population forecast has a Median Absolute Percent Error (MAPE) of 7-8%. When forecasting at a smaller geographic size, such as a county, the 10-year can grow up to 10%. It is recommended that an error rate of 4% be applied to the state’s Total Population five-year forecast. The SAP is has an even larger MAPE. It is estimated that the 5-year error rate is around 10% and should be applied to the state’s SAP forecast. Chart 5.1: Original DOLA Routt County Forecast. Major Axis is SAP. Minor Axis is Total Pop.

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The last census was in 2010. Everything since 2010 is an estimate. As Chart 5.1 clearly shows, the state demographer has the SAP estimates since 2010 growing at a much faster rate relative to the Total Population. This is highly unlikely. So not only is the five-year forecast (2017-2021) inaccurate, it is very likely that the 2011 to 2015 estimates, that the forecast are based on, are also inaccurate. Chart 5.2: Revised DOLA Routt County Forecast. Major Axis is SAP. Minor Axis is Total Pop.

The Square Cubed revised Routt County forecast flattens out the growth in SAP, as the full impact of the baby bust starts to be felt in 2019. The revised 2021 numbers are what are used for the dependent variables in the regression analysis. The full regression analysis is included in Appendix A. Below are the key data points used to forecast the 2021 K12 enrollment.

Forecast = (SAP * V1) + (Total Pop * V2) + Intercept Variable Coefficients Intercept -3468.832209

X Variable 1 (V1) 1.164941536

X Variable 2 (V2) 0.06745717

Multiple R 0.97626495 R-Squared 0.953093252 By applying the formula above to each of the revised Total Population and SAP, you will get the following forecast. Year Total Pop. SAP K12 Forecast 2017 24,871 3,727 2,550 2018 25,376 3,780 2,647

2019 26,018 3,804 2,717

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2020 26,518 3,834 2,777 2021 27,026 3,875 2,837 Please, keep in mind that for any given year’s K12 forecast, the corresponding number of students from Chart 3.1 should be removed. The reason for this is that the regression method does not take into account the SSSD residing students attending the Montessori Program. There are two main issues with using a regression method for student enrollment. First, the enrollment forecast is based off of a forecast for Total Population and SAP. In turn, the population estimates are based of estimates for years 2011 to 2015. The last good number was the 2010 census. If the population forecasts or estimates are off, there will be a larger error rate for the enrollment forecast. The second issue has to do with the fact that the regression model provides no insight into the any specific K12 enrollment trends. The biggest that comes to mind being the size of particular cohorts moving through the years. As shown in Charts 1.3 and 1.4, there is a bubble moving through the district. The regression model does not do a good job of capturing the bubble exiting the school system. Growth Rate: A second method for calculating a forecast is to apply a growth rate based on historical averages. As shown in Chart 1.2, the growth rate for SSSD has been slowing since 2013. This slow down should be accounted for in any forecasted growth rate. Below are the growth rate averages for different time frames.

2000 to 2016 1.7%

2010 to 2016 2.3%

2012 to 2016 2.1%

2014 to 2016 1.7%

Reviewing the growth rates above, a growth rate of 1.7% is the safest rate to use. If you apply the rate of 1.7% for each of the years between 2017 and 2021 you get the following products:

Year Forecast

2017 2,569

2018 2,613

2019 2,657

2020 2,702

2021 2,748

Obviously, this is a very simple method and does not take into account any nuances that might be taking place within certain grades or impacts from new schools opening.


Cohort Comparison Rate (CCR): Also known as cohort survival, is the method used by most K12 enrollment demographers. The CCR identifies the rate for any given grade by comparing that grade with the previous year’s lower grade. An example is the 2015 5th grade has 192 students. By dividing the 192 from the 2014 4th grade enrollment number of 183, a rate of 1.05 is produced. One of the drawbacks to using CCR is that kinder has no cohort. A demographer has a few options to account for this issue. One, they could simply apply a growth rate to kinder based on the historical kinder trends. This works if there are not any wild fluctuations in the number of births for any given year. However, as shown in Chart 2.1, the births for SSSD do vary greatly. In addition, we also know that there is a strong correlation between births and kinder enrollment five years later. For that reason, Square Cubed uses the birth counts gathered by the Colorado Department of Health as a proxy for the kinder cohort. Below are the grade-by-grade counts (Chart 6.1) for every year starting in 2010 and the corresponding Cohort Comparison Rates (Chart 6.2). Chart 6.1: K12 Enrollment Year Births Kin 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th Total

2010 165 161 187 201 163 163 182 170 178 174 164 159 158 173 2,233

2011 146 165 174 200 206 178 169 189 172 182 167 168 151 161 2,282

2012 161 161 185 182 196 206 185 181 193 165 179 165 171 151 2,320

2013 162 174 181 182 187 195 211 194 181 195 179 178 165 179 2,401

2014 157 190 195 188 191 183 194 213 190 190 193 190 176 175 2,468

2015 151 176 207 201 192 197 192 195 221 201 193 187 179 175 2,516

2016 154 166 162 203 193 201 192 197 204 230 203 192 190 193 2,526

Chart 6.2 Cohort Comparison Rates Year Kin 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th

2011 1.13 1.08 1.07 1.02 1.09 1.04 1.04 1.01 1.02 0.96 1.02 0.95 1.02

2012 1.00 1.12 1.05 0.98 1.00 1.04 1.07 1.02 0.96 0.98 0.99 1.02 1.00

2013 1.07 1.12 0.98 1.03 0.99 1.02 1.05 1.00 1.01 1.08 0.99 1.00 1.05

2014 1.21 1.12 1.04 1.05 0.98 0.99 1.01 0.98 1.05 0.99 1.06 0.99 1.06

2015 1.17 1.09 1.03 1.02 1.03 1.05 1.01 1.04 1.06 1.02 0.97 0.94 0.99

2016 1.08 0.92 0.98 0.96 1.05 0.97 1.03 1.05 1.04 1.01 0.99 1.02 1.08

Once the CCR’s have been identified, the demographer must decide on what CCR to use for the forecast. This is where the art comes into play. Picking the wrong CCR will have implications for all subsequent years and grades. To identify what CCR to use, Square Cubed Consulting identified the six-year average (All Year), the three-year average, and the two-year average (Chart 6.3).


Chart 6.3: Cohort Comparison Averages Average K 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th ALL YR 1.11 1.08 1.02 1.01 1.02 1.02 1.03 1.02 1.02 1.01 1.01 0.99 1.03 3 YR 1.15 1.04 1.02 1.01 1.02 1.01 1.01 1.02 1.05 1.01 1.01 0.98 1.04 2 YR 1.12 1.00 1.01 0.99 1.04 1.01 1.02 1.04 1.05 1.01 0.98 0.98 1.04

The kinder 2016 CCR of 1.08 is much lower than the previous year’s CCR. This is due to the opening of the Montessori program. Square Cubed Consulting believes that moving forward the CCR for kinder will be more in line with the 2016 rate of 1.08. The 1st grade 2016 rate of 0.92 is also due to the opening of the Montessori program. Excluding 2016, the 1st grade rate averaged 1.11 between 2011 and 2015. Square Cubed Consulting believes that the 1st grade rate moving forward will rebound nearer to the average of 1.11. This is expected because 2016 is the first year that the Montessori program opened. Moving forward it is expected that students who wish to attend the Montessori program will enter the program as kinder students. The reasoning for the 1st grade CCR also holds true for the 2nd and 3rd grade CCR’s. Reviewing the 2011 to 2015 CCR’s for 2nd grade, the average was 1.03. Three of the years were above the average. For this reason, Square Cubed Consulting expects the 2nd grade CCR to be 1.04. The 3rd grade is expected to have an average CCR of 1.03 moving forward. Again, the 2016 rate should be discounted due to the opening of the new Montessori program. Below are the CCR’s by grade that Square Cubed Consulting used to calculate the 5-year forecast (Chart 6.4). Chart 6.4: CCR’s used for Forecasting Kind 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th

1.08 1.12 1.04 1.03 1.04 1.04 1.03 1.02 1.05 1.01 1.01 1.00 1.04

The CCR’s take into account any normal development activity related to the construction of new residential units. For any given year, there are a certain number of new units constructed and closed, which will then possibly add students to the SSSD enrollment. Chart 6.5: Five-Year Forecast based on Assumed CCR’s

Birth K 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th Total

2017 135 146 186 168 209 201 208 198 201 214 232 205 192 198 2,558 2018 135 146 163 193 174 217 208 214 202 211 216 235 205 200 2,584 2019 115 124 163 170 199 180 225 214 219 212 216 219 235 213 2,589 2020 147 159 139 170 175 207 187 232 218 229 216 218 219 244 2,613 2021 150 162 178 145 175 182 214 192 236 229 242 218 218 227 2,618


The only grade where an adjustment was made was in the 9th grade. Once the Montessori program is built out, the 8th students will reenter SSSD the following 9th grade year. The expected impacts can be seen in Chart 3.1. Recommended Forecast Square Cubed Consulting suggests that SSSD uses the forecast produced from the CCR in Chart 6.5. This method accounts for all of the major factors related to enrollment forecasting. Those factors are: birth rates, historic enrollment trends, cohort bubbles, new school impact, and natural residential development. The regression forecast is a quick mathematical way to forecast enrollment. However, even though the regression model used has a very high r-squared value, it relies on future Total Population and SAP forecast to be accurate. As discussed above, Square Cubed Consulting is concerned about the original forecast provided by the state demographer. We have tried to revise them as best as possible, but the inherit risk is still great. The Growth Rate method should also be discounted. It happens to be the quickest way to produce a forecast, but also ignores major impacts such as lower birth rates and new school impacts. In the experience of Square Cubed Consulting, the Regression and Growth Rate methods should be calculated because of the ease of the calculations and to assist in framing enrollment trends. Typically, these two models over project the total enrollment. Student Yields: Student yields are calculated by geocoding current student addresses, and then dividing the number of students within a particular residential unit type by the total number of residential units by type. This allows a demographer to apply a yield to a new development to understand the impact the development will have on enrollment. It is particularly important for large developments that fall outside the historical typical development cycle. The yields are provided here so that SSSD and the committee can calculate the impact of any new development without having to contract with a developer in the future. One other note, the yields are based off of the type of unit built, not if the unit is owner occupied or being rented out. For this reason, Square Cubed Consulting thought it important to create yields based on regions. In particular, it was important to breakout the resort area from downtown. Square Cubed Consulting received a current student address file from SSSD in September 2016. The file was geocoded and successfully found each student’s address. However, students living in the county have a higher placement error (off by a certain


number of feet), then those living in the city of Steamboat Springs or near the resort. For this reason, the yields listed below for the county regions should be taken with a grain of salt. Chart 7.1 Single-Family Detached Yields

Region Students Units Yield

Resort 228 985 0.23

Downtown 592 1,473 0.40

North 327 1,088 0.30

South 108 621 0.17 The single-family detached yields are what Square Cubed Consulting expects (Chart 7.1). The yield is highest in the downtown area. In fact, the downtown yield is very similar to the single-family detached yield seen in Denver. The large number of vacation homes can explain the lower yield, for the resort region. Chart 7.2 Single-Family Attached Yields


Resort 36 1,431 0.03

Downtown 43 472 0.09

North 0 38 0

South 0 17 0

The single-family attached yields are also what Square Cubed Consulting expects for the downtown and resort areas (Chart 7.2). Chart 7.3 Condominium Yields


Resort 52 4,494 0.01

Downtown 12 631 0.02

North 0 0 0.00

South 0 43 0.00


Chart 7.4: Apartment Yields (All are in the Downtown region)

Name Students Units Yield

Hillside Village 21 90 0.23

215 Old Fish Creek 4 8 0.50

Hillcrest Apts 0 8 0.00

603 Pahwintah 3 6 0.50

Total 28 112 0.25

The KOA campground was reviewed and no students are currently residing within in the property. The mobile home park just west of the campground was also reviewed. There are 30 students living in this mobile home park. In addition, it was recommended that the western portion of Downtown be analyzed separately from the rest of downtown. The Single-family yield for this area is 0.36. The only other residential type was single-family attached. The yield for single-family attached is 0.58.


Appendix A: School by School Forecast

North Routt

Charter

Year K 1ST 2ND 3RD 4TH 5TH 6th 7th 8th 9th 10th 11th 12th Total

2017 10 12 9 11 11 11 11 11 11 0 0 0 0 97

2018 10 10 12 9 11 11 11 11 11 0 0 0 0 96

2019 10 10 10 12 9 11 11 11 11 0 0 0 0 95

2020 10 10 10 10 12 9 11 11 11 0 0 0 0 94

2021 10 10 10 10 10 12 9 11 11 0 0 0 0 93

Soda Creek Elementary

School


2017 70 93 78 112 105 110 0 0 0 0 0 0 0 568

2018 70 81 97 81 115 109 0 0 0 0 0 0 0 553

2019 58 81 85 100 83 118 0 0 0 0 0 0 0 525

2020 76 68 84 87 102 86 0 0 0 0 0 0 0 503

2021 78 87 71 87 89 107 0 0 0 0 0 0 0 519

Strawberry Park

Elementary School


2017 66 81 81 86 85 87 0 0 0 0 0 0 0 486

2018 66 72 84 84 91 88 0 0 0 0 0 0 0 485

2019 56 72 75 87 88 96 0 0 0 0 0 0 0 474

2020 73 61 76 78 93 92 0 0 0 0 0 0 0 473

2021 74 81 64 78 83 95 0 0 0 0 0 0 0 475

Steamboat Springs Middle School


2017 0 0 0 0 0 0 187 190 203 0 0 0 0 580

2018 0 0 0 0 0 0 203 191 200 0 0 0 0 594

2019 0 0 0 0 0 0 203 208 201 0 0 0 0 612

2020 0 0 0 0 0 0 221 207 218 0 0 0 0 646

2021 0 0 0 0 0 0 183 225 218 0 0 0 0 626

Steamboat Springs

High School


2017 0 0 0 0 0 0 0 0 0 231 200 184 187 802

2018 0 0 0 0 0 0 0 0 0 215 230 197 189 831

2019 0 0 0 0 0 0 0 0 0 215 214 227 202 858

2020 0 0 0 0 0 0 0 0 0 215 213 211 233 872

2021 0 0 0 0 0 0 0 0 0 241 213 210 216 880

Yampa Valley School


2017 0 0 0 0 0 0 0 0 0 1 5 8 11 25

2018 0 0 0 0 0 0 0 0 0 1 5 8 11 25

2019 0 0 0 0 0 0 0 0 0 1 5 8 11 25

2020 0 0 0 0 0 0 0 0 0 1 5 8 11 25

2021 0 0 0 0 0 0 0 0 0 1 5 8 11 25


Appendix B: Birth Data

Cohort Year Births

2000-01 94

2001-02 105

2002-03 94

2003-04 99

2004-05 110

2005-06 150

2006-07 119

2007-08 119

2008-09 132

2009-10 120

2010-11 165

2011-12 146

2012-13 161

2013-14 162

2014-15 157

2015-16 151

2016-17 154

2017-18 135

2018-19 135

2019-20 115

2020-21 147

2021-22 150

Note: The 2021 cohort year corresponds with 2016. The 150births is an estimate.


Appendix C: Out of District Counts

Year K12

Count

2007 48

2008 45

2009 56

2010 115

2011 104

2012 109

2013 111

2014 122

2015 129

2016 142

2016 by Grade

Kinder 9

1 10

2 12

3 13

4 15

5 9

6 8

7 7

8 14

9 11

10 11

11 10

12 11

Total 140


Appendix A: Regression Analysis

Regression Statistics Multiple R 0.971675552 R Square 0.944153378 Adjusted R

Square 0.93556159 Standard Error 52.88720633 Observations 16

ANOVA

df SS MS F Significance

F

Regression 2 614738.2643 307369.1321 109.8902085 7.16935E-

09

Residual 13 36361.73571 2797.056593 Total 15 651100

Coefficients Standard

Error t Stat P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept -3468.832 583.461 -5.945 0.000 -

4729.323 -

2208.341 -

4729.323 -

2208.341

X Variable 1 1.165 0.265 4.394 0.001 0.592 1.738 0.592 1.738

X Variable 2 0.067 0.021 3.287 0.006 0.023 0.112 0.023 0.112

RESIDUAL OUTPUT

PROBABILITY OUTPUT

Observation Predicted Y Residuals

Percentile Y

2000 1902.929499 44.07050103

3.125 1911 2001 1905.820353 5.179647007

9.375 1912

2002 1972.134164 39.13416362

15.625 1930 2003 1949.249179 37.24917859

21.875 1933

2004 1938.738371 8.738370752

28.125 1947 2005 1964.02474 14.9752602

34.375 1979

2006 2021.876908 0.876908491

40.625 2021 2007 2112.150237 35.15023722

46.875 2077

2008 2175.877564 33.87756413

53.125 2142 2009 2217.097655 65.09765507

59.375 2152

2010 2278.936818 45.93681753

65.625 2233 2011 2218.226366 63.77363361

71.875 2282

2012 2230.221221 89.778779

78.125 2320 2013 2317.321862 83.67813758

84.375 2401

2014 2449.054241 18.94575879

90.625 2468

2015 2570.340822 -54.3408218

96.875 2516


Strawberry Park Elementary School Scatter Plot


Steamboat Springs Middle School Scatter Plot


Steamboat Springs High School Scatter Plot


North Routt Charter School Scatter Plot


Soda Creek Elementary School Scatter Plot

Soda Creek Elementary School Scatter Plot


Yampa Valley High School Scatter Plot

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