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Unformatted text preview: Announcements Midterm Thursday, 10/20 in OML202 – • Closed note, closed book. Any complicated formulas needed will be provided. • Bring a calculator Next week – • Go to sections for remainder of the term • EXCEPTION : PreMed section meets with me and 103 section just for Tuesday, October 25 (David Salsburg is at a meeting in Nevada ) • Classrooms posted on website After this week, you should go to TA’s for your sections STAT 101106a Introduction to Statistics 250 Note : • o β is the Yintercept : the value of Y when X is zero. • Our estimate of o β is o b the CONSTANT. • While MINITAB provide a test of whether or not this intercept is zero, you should almost alwa IGNORE THIS TEST. Leave the intercept in the model even if it is not significant!! • REASON : Unless you have some reason to think that Y should be zero when X is zero, the constant simply allows the line to fit better! Example : Climate Data. Regression Analysis The regression equation is Mean =  32.6 + 0.0302 year Predictor Coef StDev T P Constant 32.64 15.18 2.15 0.034 year 0.030172 0.007782 3.88 0.000 S = 1.854 RSq = 14.9% RSq(adj) = 13.9% STAT 101106a Introduction to Statistics 251 This is b This is t obs for b This is the s.d. of b IGNORE THIS pvalue!!! 8 442 0 2 4 i o i X Y 1 β β + = Yintercept o β 5. Check Model Assumptions Here again is our hypothesized regression model : i i o i X Y ε β β + + = 1 , ) , ( ~ σ ε N i This model has two main assumptions : 1) The relationship between X and Y is linear 2) The errors have an approximately normal distribution These assumptions can both be checked by examining RESIDUAL PLOTS! Examing Residuals in MINITAB : When performing regression using Stat Regression Regression , click on Graphs . Various plots are listed, but for a complete set, click on 4 in 1. STAT 101106a Introduction to Statistics 252 Example : ND Temperature Data Model Remember that a good way to see if data is normally distributed is the normal quantile plot . This plot is a normal quantile plot of the residuals. It should look like a line. This is a plot of the residuals vs. the fitted values. If the model fits well, this should be a formless blob . If there are patterns, then some model assumption has been violated. Also, this plot is useful for detecting outliers from the regression This plot is simply a histogram of the residuals. It’s a less useful way to see if This is a plot of residuals by the order of the data. In our case, the data is in order of STAT 101106a Introduction to Statistics 253 Residual Percent 5.0 2.5 0.02.55.0 99.9 99 90 50 10 1 0.1 Fitted Value Residual 27 26 25 5.0 2.5 0.02.55.0 Residual Frequency 4 224 20 15 10 5 Observation Order Residual 80 70 60 50 40 30 20 10 1 5.0 2.5 0.02.55.0 Normal Probability Plot of the Residuals Residuals Versus the Fitted Values Histogram of the Residuals Residuals Versus the Order of the Data Residual Plots for Avg Min Monthly Temp the residuals have a normal...
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 Fall '05
 JonathanReuningSchererDonaldGreen
 Normal Distribution, Regression Analysis, Errors and residuals in statistics, residuals, Observat ion Order

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