The following output (from MINITAB) is for the least-squares fit of the model ln y = 0 + 1 ln x + , where y represents the monthly production of a gas well and x represents the volume of fracture fluid pumped in. (A scatterplot of these data is presented in Figure 7.22.) Regression Analysis: LN PROD versus LN FLUID The regression equation is LN PROD = 0.444 + 0.798 LN FLUID Predictor Coef SE Coef T P Constant 0.4442 0.5853 0.76 0.449 LN FLUID 0.79833 0.08010 9.97 0.000 S = 0.7459 RSq = 28.2% RSq(adj) = 27.9% Analysis of Variance Source DF SS MS F P Regression 1 55.268 55.268 99.34 0.000 Residual Error 253 140.756 0.556 Total 254 196.024 Predicted Values for New Observations New Obs Fit SE Fit 95.0% CI 95.0% PI 1 5.4457 0.0473 ( 5.3526, 5.5389) ( 3.9738, 6.9176) Values of Predictors for New Observations New Obs LN FLUID 1 7.3778 a. What is the equation of the least-squares line for predicting ln y from ln x? b. Predict the production of a well into which 2500 gal/ft of fluid have been pumped. c. Predict the production of a well into which 1600 gal/ft of fluid have been pumped. d. Find a 95% prediction interval for the production of a well into which 1600 gal/ft of fluid have been pumped. (Note: ln 1600 = 7.3778.)
STAT 2004 WEEK 14 REVIEW: T-test Use a T-test when sigma is unknown. Use cutoffs to test, not p-values. HYPOTHESIS TESTING RATIONALE Make an assumption. Is what you observed likely or unlikely Compare what you observe to what you expect. CHI-SQUARE TEST How different is what we observed from what we expected 2 For each category, calculate (observed−expected) . Add these values expected together for the chi-square value. The degrees of freedom for a chi-square value is the number of categories minus 1. o Look up the actual chi-square value on the table. o Is the ch
