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- Title: stat3411_old_exam_ch_4_1_4_2
- Type: Notes
- School: Minnesota
- Course: STAT 3411
- Term: Fall
Coursehero >> Minnesota >> Minnesota >> STAT 3411
Path: Minnesota >> STAT >> 3411 Fall, 2008
Path: Minnesota >> CHRI >> 1010 Fall, 2008
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Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
Path: Minnesota >> STAT >> 5411 Fall, 2008
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Path: Minnesota >> STAT >> 2411 Fall, 2008
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Path: Minnesota >> STAT >> 2411 Fall, 2008
Path: Minnesota >> STAT >> 2411 Fall, 2008
Path: Minnesota >> STAT >> 2411 Fall, 2008
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3411 Stat Exam Questions Section 4.1 & 4.2 (1) (Sp 2006) Fitting a least squares line to 3 points gives the following values of Y and the fitted line Y = b0 + b1X Y 10 20 60 Y 5 10 45 Residual _ ________ ________ (a) Fill in values for the residuals. (b) Find the value of R2 (2) (Sp 2006) We are fiiting a regression with ln(y), x1 and x2. ln(Y ) = b0 + b1X1 + b2X2 The variable y is breaking strength. The fitted equation has coefficients Intercept x1 x2 b0 b1 b2 2.16559 21.64888 -0.30338 (a) What is the predicted value of y (not ln(y)) if x1 = 0.250 x2 = 12.000 (b) What is the effect on the breaking strength, y, of increasing x2 by 4 (regardless of the value for x1) ? (3) (Fall 2006) A variable y potentially depends on variables x1 and x2. For a fixed value of x1 it is anticipated that a 10% increase in x1 will result in a 2% increase in y. For a fixed value of x2 it is anticipated that an increase of 5 units in x1 will result in a 20% decrease in y. What function would you anticipate fitting to these data? You do not have to give any values for the coefficients of the equation, just give the form of the regression equation you would use with regression coefficients b0, b1, and b2. Explain briefly how you choose this model. (4) (Fall 2006) The following means are from an experiment studying the axial breaking strength (y) of wooden dowels as a function of diameter (x1) and length (x2). Diameter 0.125 0.125 0.125 0.1875 0.1875 0.1875 0.250 0.250 0.250 Length 4 8 12 4 8 12 4 8 12 Mean Strength 51.7 6.7 2.6 220.8 71.3 19.1 342.4 153.0 56.3 (a) What is the first thing to do with these data along the path of analyzing the data? (b) Does it appear that the equation y = b0 + b1 x1 + b2 x 2 a reasonable model for these data? Explain you answer and show how you decided. (c) If you decided that the model in part (b) won t work well, what might you do to improve the model for fitting these data? (5) (Fall 2006) A variable y potentially depends on variables x1 , x2 and x3. After fitting a potential model to the data, how would you decide how well this model fits the data? What numerical and graphical summaries would be helpful in assessing the fit of this model to the observed data? (6) (Sp 2007) After fitting the model Y b0 + b1X1 + b2X2 to data, what is the purpose of inspecting residual plots? You do not have to describe residual plots or how you interpret them. Just tell me we what expect to accomplish by inspecting residual plots. (7) (Sp 2007) We have collected data on the torque (Y) required to rotate a drill with various diameters (X1) and feed rates (X2). In developing a model for predicting required torque based on diameter and feed rate, there are man possible equations that could be used. For example Y b0 + b1X1 + b2X2 Log(Y) b0 + b1X1 + b2X2 Log(Y) b0 + b1log(X1) + b2log(X2) Y b0 + b1X1 + b2X2 + b3(X1)2 + b4(X2)2 + b5X2X1 Whatever model we fit to the data should fit the observed data reasonably well and the residual plots should pass inspection. What else would you consider in choosing the final model other than how well the model fits the data? (A short, clear answer is fine.) (8) (Sp 2007) For predicting wear life (Y) of a film lubricant from speed (X1) and load (X2) we find the fitted equation ln (Y) 20.5 1.2*ln (X1) 1.4* ln (X2) (a) Write the corresponding fitted equation for Y in simplest form. Y (b) What is the effect on wear life associated with a doubling of the speed? (9) The following plot is from a regression analysis to model wear life of a textile. (a) What problems are indicated by this plot? (b) What would do next in your analysis of these data? (10) We fit three points with the equation y 1 3 2 y = b0 + b1 x resulting in y 1.5 2 2.5 As always, show how you find your answers to the following questions. Give final numerical answers. (a) Find the sum of squared residuals. (b) Find (c) Find R2 ( y y ) i 2 (11) For predicting Y from X1 , X2 and X3 ,we find the fitted equation ln (Y) 12 0.75*X1 0.35* X2 + 0.53* X3 At the current process settings the predicted value of Y is 545. If we leave X2 and X3 unchanged, but increase X1 by 0.25, what is the predicted value of Y ( not ln (Y) ) under these new conditions? Give a final numerical answer. (12) In another project predicting Y from X1 and X2 , we anticipate a power model y 0 X 1 1 X 2 2 How could we use Excel to estimate the values for 0 , 1 , and 2 ? (13) We are predicting Y=lifetimes of a particular material. In predicting Y from X1 and X2 , we fit the model Y b0 + b1X1 + b2X2 and check some residual plots. (a) What three problems are indicated by this residual plot versus predicted values? (b) What does this residual plot tell us? (c) What could we do to try fixing the problems seen here?
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LA8741_Assignments_011306.pdfPath: Minnesota >> LA >> 8741 Fall, 2008
Description: LA 8741 Metropolitan Design Workshop, 2006 Academic Health Center Precinct Planning Short Assignment 1: Urban Expedition Due: Jan 25 This assignment is intended to capture your first impressions of the study area, and for the instructors to learn abo...
LA8741_Final.pdfPath: Minnesota >> LA >> 8741 Fall, 2008
Description: Academic Health Center Master Plan Acknowledgements Suggested citation: Metropolitan Design Workshop, 2006. Master Plan for the Academic Health Center at the University of Minnesota. Minneapolis: University of Minnesota, Department of Landscape Arch...
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IMA-2008.pptPath: Minnesota >> IMA >> 2008 Fall, 2008
Description: A consistent multiscale bridge connecting atomistic and coarse-grained models QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. W. G. Noid Department of Chemistry Penn State University Acknowledgements Prof. Gregory A...
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minnesota08.pdfPath: Minnesota >> IMA >> 08 Fall, 2008
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Heading Home Hennepin Plan.pdfPath: Minnesota >> BLOG >> 068 Fall, 2008
Description: Photography: Cathy ten Brooke Cover Design: Brandon Cotton Produced by Hennepin County Public Affairs Department Table of Contents Introduction/Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
Heading Home Hennepin update.pdfPath: Minnesota >> BLOG >> 068 Fall, 2008
Description: THE 10-YEAR PLAN TO END HOMELESSNESS IN MINNEAPOLIS AND HENNEPIN COUNTY Report to the Heading Home Hennepin Executive Committee: Implementation on first year benchmarks as of August, 2007 Goal One: Prevent Homelessness 1.1.1 Expand Hennepin County ...
04summary.pdfPath: Minnesota >> SWROC >> 2004 Fall, 2008
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stat2411_exam_1_A.pdfPath: Minnesota >> STAT >> 2411 Fall, 2008
Description: 1000 (1) Find the numerical value of . 2 (2) How many ways can we arrange 3 of 5 paintings horizontally on a wall? (3) A primary election has 10 candidates. How many ways can we choose 2 of the candidates for the final election? (4) A cage has 12 m...
Copy of bio200presentationPath: SUNY Buffalo >> BIO >> 200 Fall, 2007
Description: Bruce Ruchalski Cory Trybushyn Joe Kapanek Steven Blount and Kaushal Amin Rank and Dominance/Hierarchy Pan troglodyte Pan paniscus Chimpanzee Bonobo What is a Bonobo? Biologically speaking, bonobos are the closest you can get to being hum...
stat2411_exam_1_A_ans.pdfPath: Minnesota >> STAT >> 2411 Fall, 2008
Description: Stat 2411 Exam 1 A 1) 2) 3) 4) 5) 1000 999 = 499,500 2 5 4 3 = 60 (10 ) = 45 2 440 (12 )(10 ) 3 1 = 0.30 22 = ( 4 ) 1463 Aside: I will never ask you for this sort of solution, but here is how the problem is done (in more advanced course) without...
stat2411_exam_1_B.pdfPath: Minnesota >> STAT >> 2411 Fall, 2008
Description: For each problem show how you arrive at your final answer. You can leave answers as unsimplified numerical expressions. If you have time, you may want to find the final answer to see if it makes sense. You may not leave answers with expressions such ...
stat2411_exam_1_B_ans.pdfPath: Minnesota >> STAT >> 2411 Fall, 2008
Description: Stat 2411 Exam 1 B (1) The population mean is represented by the symbol and the population standard deviation is represented by the symbol . (2) histogram (3) (a) (b) (4) (5) 45 + 1 = 23 Median = 191 2 (ii) 12mm Position 1 90 +1 85 + 2 80 1+1...
stat2411_exam_1_C.pdfPath: Minnesota >> STAT >> 2411 Fall, 2008
Description: You can leave any answers as un-simplified expressions such as 1000 2 C5 P4 (1.3 + 2.4 + 5.3)/3 4x3/(52x51) 10 30 but you do need to explain/show how you got to your answer. (1) A student had the following GPAs in 4 semesters in college. Seme...
stat2411_exam_1_C_ans.pdfPath: Minnesota >> STAT >> 2411 Fall, 2008
Description: Stat 2411 Exam 1 C (1) (2) (3) Weighted mean 20 19 18 12(3.2) + 15(3.4) + 14(3.0) + 16(3.6) 12 + 15 + 14 + 16 0.55 + 0.56 = 0.555 2 P(at least 1) = P(1) + P(2) + P(3) + P(4) (4) 40 (10 )( 40 ) + (10 )( 40 ) + (10 )(1 ) + (10 ) 2 2 3 4 =1 3 ( 50 )...
stat2411_exam_1_D.pdfPath: Minnesota >> STAT >> 2411 Fall, 2008
Description: Except for problem 1, you can leave answers as unsimplified numerical expressions. Expressions include for example 1.2 + 1.3 + 1.8 3 10C5 30P4 (1 3) 2 + (3 3) 2 + (5 3) 2 10 5 (1) Find the geometric mean of 4, 8, 16. Find the final number, n...