1. Linear Regression Statistics & Risk Management Copyright © Texas Education Agency, 2012. All rights reserved. 1

2. 2 “Copyright and Terms of Service Copyright © Texas Education Agency. The materials found on this website are copyrighted © and trademarked ™ as the property of the Texas Education Agency and may not be reproduced without the express written permission of the Texas Education Agency, except under the following conditions: 1)Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts’ and schools’ educational use without obtaining permission from the Texas Education Agency; 2) Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of the Texas Education Agency; 3) Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way; 4) No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from the Texas Education Agency and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty fee. Call TEA Copyrights with any questions you have.

3. Copyright © Texas Education Agency, 2012. All rights reserved. Beyond Correlation If you have a strong correlation you may be able to predict outcomes. If you have a strong correlation you may be able to predict outcomes. 3

4. Copyright © Texas Education Agency, 2012. All rights reserved. Collect Data RainYieldRainYieldRainYieldRainYield 22.36103.74100.8059.58 6.0943.6441.4770.62 93.6722.5085.6081.66 62.4475.3990.5193.69 84.7229.3027.1499.71 14.2476.6118.3214.14 52.3320.2948.2151.41 69.6129.3837.5475.66 104.6650.5367.706.18 56.6720.212.062.10 31.4236.2953.4721.18 17.3950.5670.5517.17 7.259.136.0787.63 90.6997.6614.0996.58 46.4233.1860.5461.42 36.3920.06 ---- 4

5. Copyright © Texas Education Agency, 2012. All rights reserved. Charted 5

6. Establish Line 6

7. Copyright © Texas Education Agency, 2012. All rights reserved. Analysis 60 inches of rain? 60 inches of rain? 90 inches of rain? 90 inches of rain? 120 inches of rain? 120 inches of rain? Could we plateau out? Could we plateau out? Could we eventually have too much rain? Could we eventually have too much rain? 7