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A set of exam questions and solutions related to regression analysis. The questions cover topics such as response variable identification, least squares regression line calculation, estimated error variance, residuals and studentized residuals, prediction of impurity percentage in oxygen, and hypothesis testing. The document also includes sas output for reference.

Typology: Exams

2011/2012

1 / 10

Download Regression Analysis Exam Questions and Solutions and more Exams Statistics in PDF only on Docsity! STAT 512 EXAM I STAT 512Name (5 pts) Problem Points S ore1 472 203 28 USE YOUR TIME WISELYSHOW YOUR WORK TO RECEIVE PARTIAL CREDITWRITE LEGIBLY. ANYTHING UNREADABLE WILL NOT BE GRADEDGOOD LUCK!!!! 1. A plant distills liquid air to produ e oxygen. The following data were used by this plantto assess the relationship between the per entage of impurity in the oxygen(PERC) with the amount (ppm) of impurity in the liquid air (AMT). Use theatta hed SAS output at the end of the exam and the s atterplot below to answer thefollowing questions. (a) (3 pts) What is the response variable?(b) (6 pts) Write down the least squares regression line and des ribe the relationship be-tween PERC and AMT. 2. Short answer questions. Ea h part is unrelated.(a) (3 pts) Suppose the estimated regression equation is bY = 2+ 3X. Give the estimatedregression equation if the variable U = 3X + 6 were used in pla e of X. (b) (4 pts) Explain how a 95% on den e interval for the slope an be used to test H0 : 1 = 5 at the = :05 level? ( ) (5 pts) Rob Poorman Auto Sales has de ided to use R2 to sele t the best model inpredi ting ar demand based on several demographi variables. Explain when (andwhen not) this is a reasonable approa h. (d) (8 pts) For ea h of the following residual plots (ei vs bY ), state whi h assumptions ofthe linear regression model (if any) appear violated. • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0.2 0.4 0.6 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 • • • • • • • • •• • • • • • • • • • • • •• • • • • • • • •• • • • ••• 5.4 5.6 5.8 -0.5 0.0 0.5 1.0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 5.4 5.5 5.6 5.7 -0.2 0.0 0.2 0.4 • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • •• • • •• • • 5.40 5.45 5.50 5.55 -6 -4 -2 0 2 4 6 3. An experiment was performed to best predi t the burn time of a toba o leaf using the leafper entages of nitrogen (X1), hlorine (X2), and potassium (X3). Use the atta hed SASoutput of the top 10 \best" models to answer the following questions.(a) (4 pts) The log(burn time) was hosen as the response variable. Des ribe a possiblereason for using this transformation of burn time? (b) (4 pts) The full model ontained all the quadrati terms and rst-order intera tions(e.g., X21 and X1X2). Prior to analysis, the original variables were standardized. Whywas this done? ( ) (4 pts) Write down the tted regression line for the best model based on adjusted R2. (d) (6 pts) Explain what this regression line tells you about the relationship between theper entages of the three elements and the burning time.

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