Washington State University



Correlation and RegressionExample Studies have shown that people who suffer sudden cardiac arrest (SCA) have a better chance of survival if a defibrillator is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? This question is addressed in the paper “Improving Survival from Sudden Cardiac Arrest: The Role of Home Defibrillators” (by J.K. Stross, University of Michigan, February 2002). The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitative center (where cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes.Mean call-to-shock time,x267912Survival Rate, y90453052Entering data into Minitab:Mean call-to-shock time, xSurvival rate, y29064573095122Calculating Pearson Correlation CoefficientMinitab Commands: STAT > BASIC STATISTICS > CORRELATION > double click on the two variables > OKOutput:Pearson correlation of x and y = -0.960Determine the Equation for the Least Squares Regression Line and Conducting Hypothesis Test for the Slope ParameterMinitab Commands: STAT > REGRESSION > REGRESSION > FIT REGRESSION MODEL > y is the response variable and x is the continuous predictor > OK.Output:Analysis of VarianceSource DF Adj SS Adj MS F-Value P-ValueRegression 1 4735.2 4735.2 35.34 0.010 x 1 4735.2 4735.2 35.34 0.010Error 3 402.0 134.0Total 4 5137.2Model Summary S R-sq R-sq(adj) R-sq(pred)11.5760 92.17% 89.57% 62.01%CoefficientsTerm Coef SE Coef T-Value P-Value VIFConstant 101.3 12.4 8.18 0.004x -9.30 1.56 -5.94 0.010 1.00 Regression Equationy = 101.3 -?9.30?xScatterplot with regression LineMinitab Commands: STAT > REGRESSION > FITTED LINE PLOTOutput:Confidence Interval for the mean of y and Prediction Interval for y if x=6Minitab Commands: STAT > REGRESSION > REGRESSION > PREDICT > Enter 6 for xOutput:Prediction for y Regression Equationy = 101.3 -?9.30?xVariable Settingx 6 Fit SE Fit 95% CI 95% PI45.5547 5.50654 (28.0305, 63.0790) (4.75910, 86.3504)Assessing Reasonableness of AssumptionsSTAT > REGRESSION > REGRESSION > FIT REGRESSION MODEL > y is the response variable and x is the continuous predictor > GRAPHS > Click on Normal probability plot of residuals and residuals vs fits > OK > OK ................
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