1. © Buddy Freeman, 2015 Regression Interval Estimates

2. © Buddy Freeman, 2015 Confidence Interval Estimates Consider X i = 8 commercials. There are an infinite number of water consumption values that correspond to X i = 8 commercials. What is the mean of all of THESE water consumption values? Another way to ask the question is, “What is the average consumption of water when there are 8 commercials?”. The symbol for the mean of all the Y values that correspond to a specific X value is  Y|X.

3. © Buddy Freeman, 2015 Prediction Interval Estimates Consider X i = 8 commercials. There are an infinite number of water consumption values that correspond to X i = 8 commercials. The next time that there are 8 commercials we would like to predict what the SPECIFIC water consumption will be? The sample regression formula gives us. It is but one value out of an infinite number of possibilities. The formula given above “reaches out” on both sides of far enough to give us the desired level of confidence that the next water consumption level corresponding to 8 commercials will be within that interval.

4. © Buddy Freeman, 2015 Prediction Interval Estimate Confidence Interval Estimate

5. © Buddy Freeman, 2015 X y i -hat CI-IncrementPI-IncrementCI-lowerCI-upperPI-lowerPI-upper 74,267.857784.7481,725.6633,483.1095,052.6052,542.1945,993.520 85,178.571636.3401,663.4344,542.2315,814.9113,515.1386,842.005 96,089.286527.6251,624.9535,561.6606,616.9114,464.3337,714.239 107,000.000486.0131,611.9226,513.9877,486.0135,388.0788,611.922 117,910.714527.6251,624.9537,383.0898,438.3406,285.7619,535.667 128,821.429636.3401,663.4348,185.0899,457.7697,157.99510,484.862 139,732.143784.7481,725.6638,947.39510,516.8918,006.48011,457.806 1410,642.857954.5101,809.1919,688.34711,597.3678,833.66612,452.048 Numbers in the Relevant Range

6. © Buddy Freeman, 2015 { Relevant Range Extrapolation { Interpolation

7. © Buddy Freeman, 2015 Xy i -hatCI-IncrementPI-IncrementCI-lowerCI-upperPI-lowerPI-upper 74,267.857784.7481,725.6633,483.1095,052.6052,542.1945,993.520 CI-lower = 3,483.109 and CI-upper = 5,052.605

8. © Buddy Freeman, 2015 Xy i -hatCI-IncrementPI-IncrementCI-lowerCI-upperPI-lowerPI-upper 74,267.857784.7481,725.6633,483.1095,052.6052,542.1945,993.520 PI-lower = 2,542.194 and PI-upper = 5,993.520