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### 501_Lecture_02

Course: STAT 501, Spring 2012
School: Purdue University -...
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Word Count: 1545

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2.1-2.2 Looking Sections at Data-Relationships Data with two or more variables: Response vs Explanatory variables Scatterplots Correlation Regression line Association between a pair of variables Association: Some values of one variable tend to occur more often with certain values of the other variable Both variables measured on same set of individuals Examples: Height and weight of same individual...

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2.1-2.2 Looking Sections at Data-Relationships Data with two or more variables: Response vs Explanatory variables Scatterplots Correlation Regression line Association between a pair of variables Association: Some values of one variable tend to occur more often with certain values of the other variable Both variables measured on same set of individuals Examples: Height and weight of same individual Smoking habits and life expectancy Age and bone-density of individuals Causation? Caution: Often there are spurious, other variables lurking in the background Shorter women have lower risk of heart attack Countries with more TV sets have better life expectancy rates More deaths occur when ice cream sales peak Just explore association or investigate a causal relationship? Preliminaries: Who are the individuals observed? What variables are present? Quantitative or categorical? Association measures depend on types of variables Response variable measures outcome of interest Explanatory variable explains and sometimes causes changes in response variable Examples Different amount of alcohol given to mice, body temperature noted (belief: drop in body temperature with increasing amount of alcohol) Response variable? Explanatory variable? SAT scores used to predict college GPA Response variable? Explanatory variable? Examples Does fidgeting keep you slim? Some people don't gain weight even when they overeat. Perhaps fidgeting and other "nonexercise activity" explains why, here is the data: We want to plot Y vs. X Which is Y? Which is X? Things to look for on scatterplot: Form (linear, curve, exponential, parabola) Direction: Positive Association: Y increases as X increases Negative Association: Y decreases as X increases Strength: Do the points follow the form quite closely or scattered? Outliers: deviations from overall relationship Let's look again... Example: State mean SAT math score plotted against the percent of seniors taking the exam Adding a categorical variable or grouping May enhance understanding of the data Categorical variable is (region): "e" is for northeastern states "m" is for midwestern states All others states excluded Example: Adding categorical variable Other things: Plotting different categories via different symbols may throw light on data Read examples 2.7-2.9 for more examples of scatterplots Existence of a relationship does not imply causation SAT math and SAT verbal scores have strong relationship But a person's intelligence is causing both The relationship does not have to hold true for every subject, it is random 2.2 Correlation Linear relationships are quite common Correlation coefficient r measures strength and direction of a linear relationship between two quantitative variables X and Y Data structure: (X,Y) pairs measured on n individuals Weight and blood pressure Age and bone-density Correlation (r) Lies between -1 and 1 If switch roles of X and Y r remains the same Unit free, unaffected by linear transformation Positive correlation means positive association negative correlation means negative association X and Y should both be quantitative r near 0 implies weak (or no) linear relationship; closer to +1 or -1 suggests very strong linear pattern Formula: r = 1 xi - x yi - y s s n -1 x y Calculation: Usually by software or calculator Calculate means and standard deviations of data Standardize X and Y: take off respective mean divide by corresponding standard deviation Take products of X(standardized)*Y (standardized) for each subject Add up and divide by n-1 Issues: r is affected by outliers Captures only the strength of the "linear" relationship it could be true that Y and X have a very strong non-linear relationship but r is close to zero r = +1 or -1 only when points lie perfectly on a straight line. (Y=2X+3) SAS program: correlation.doc proc corr is the procedure Summary Scatterplots: look for form, direction, strength, outliers Correlation: Numerical measure capturing direction and strength of a linear relationship Sign of r: direction Value of r: strength Always: Plot the data, look at other descriptive measures along with the correlation Sections 2.3-2.4 Looking at Data-Relationships 2.3 Regression Line Straight line which describes best how the response variable y changes when the explanatory variable x changes We do distinguish between Y and X cannot switch their roles Equation of straight line: y = a + b x a is the intercept (where it crosses the y-axis) b is the slope (rate) Procedure calculate best a and b for your data Find the line that best fits your data Use this line to predict y for different values of x Example: Regression line for NEA data. We can predict the mean fat gain at 400 calories Prediction and Extrapolation Fitted line for NEA data: Pred. fat gain = 4.505 0.00344(NEA) Prediction at 400 calories: Pred. fat gain = 4.505 0.00344*400 = 2.13 kg So when a person's NEA increases by 400 calories when overeat, they they will have a predicted fat gain of 2.13 kilograms. Prediction and Extrapolation Warning: Extrapolation--predicting beyond the range of the data--is dangerous! Prediction at 1500 calories Pred. fat gain = 4.505 0.00344*1500 = -1.66 kg So predicting for a 1500 NEA increase when overeating, the prediction is that they will lose 1.66 kilograms of weight Not trustworthy Far outside the range of the data Least Squares Regression (LSR) Line The line which makes the sum of squares of the vertical distances of the data points from the line as small as possible y is the observed (actual) response is the predicted response by using the line Residuals Error in prediction y Formula for Least Squares Regression line Given (explanatory x, response y): Calculate x, y, s x , s y , and r. intercept = a = y - bx slope = b = r sy sx y = a + bx ^ Example: (Egypt data) x = 324.8 calories s x = 257.66 calories y = 2.388 kg s y = 1.1389 kg r = - 0.7786 b=r sy sx a = y - bx ^ y= Using the formula: Slope: b = -.7786 * 1.1389/257.66 = -0.00344 Intercept: a = (mean of y) slope * (mean of x) = 2.388 (-0.00344)*324.8 = 3.505 Regression line: Predicted fat gain = 3.505 0.00344*cal = 3.505 0.00344x Example: Predicted values and Residuals Predicted fat gain for observation 2 (-57 cal.) 2 = 3.505 0.00344*(-57) = 3.70108 kg Observed fat gain: y2 = 3.0 kg Residual or error in prediction = y2 - 2 = 3.0 3.70108 = -0.70108 kg Residual practice Residual is yi i For NEA data observation 15 has NEA = x15 = 580 Find the predicted value, 15 Find the residual, y15 - 15 Properties of regression line Cannot switch Y and X Passes through the mean of x and mean of y Physical interpretation of the slope b: with one unit increase in X, how much does Y change on average? Example: NEA data: with 1 calorie increase in NEA, fain gain changes by -0.00344 kg How about 100 increase in NEA? Properties (cont.) Sign of slope (b) is sign of correlation (r) captures the direction of linear association Slope b is affected by scale change but not by a shift (adding or subtracting a constant from all data points) Convert: X from months to years Let's say the slope is 5, when using months What would the slope be if we used years for X instead? If Y increases by 5 per month, it'll increase by ? per year? Using software SAS will evaluate the least squares regression line but you have to know where to find them in the output Residuals and predicted values are also printed SAS program : regression.doc the regression procedure is proc reg We will do a deeper analysis of regression in chapter 10 Correlation and Regression In correlation, X and Y are interchangeable, NOT so in regression. Slope (b), depends on correlation (r) R2--Coefficient of Determination Square of correlation Fraction of variation in y explained by LSR line Higher R2 suggests better fit Example: R2 = 0.6062 for NEA data means that 60.62% of the unexplained variation in fat gain is explained by your fitted regression line with x = NEA. R2--another example Explains the part of the variation of y which comes from the linear relationship between y and x. In this case between Height and Age. less spread tight fit R2 = 0.989 more scatter more error in prediction R2 = 0.849 2.4 Caveats about correlation & regression Residuals can tell us whether we have a good fit Residual = observed y - predicted y Used to assess the fit of regression line Residual plot: plot of residuals vs x Residuals add up to zero and have a mean of zero Thus, a fit is considered good if the plot shows a random spread of points about the zero line but without any definitive pattern Residual plot Scatterplot of residuals against explanatory variable Helps assess the fit of regression line Outliers and influential observations Outliers: Lies outside the pattern of other observations Y-outliers: large residual X-outliers: often influential in regression Influential points: Deleting this point changes your statistical analysis drastically pull the regression line towards themselves Least squares regression is NOT robust to presence of outliers Example: Gesell data r = 0.4819 Subject 15: Y-outlier Far from line High residual X-outlier Close to line Small residual Subject 18: Example: Gesell data r = 0.4819 Drop 15: r = 0.5684 Drop 18: r = 0.3837 Both have some influence, but neither seems excessive Causation Association does not imply causation! An association between x and y, even if it is very strong, is not itself good evidence that changes in x actually cause changes in y. Causation: Variable X directly causes a change in Variable Y Example: X = plant food Common Response Other variables may affect the relationship between X and Y Beware of lurking variables Example: for children, X = height Y = Math Score Z = Age Confounding Other variables may affect the relationship between X and Y Can't separate effects of X and Z on Y Example: X = number years of education Y = income Z = ??
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Purdue University - Main Campus - STAT - 501
Chapter 2 highlightsAssociation and CausationAssociation between a pair of variablesAssociation: Some values of one variable tend to occur more often with certain values of the other variable Both variables measured on same set of individuals Examples:
Purdue University - Main Campus - STAT - 501
Section 5.2Sampling Distribution for Counts and ProportionsPreviewPopulation distribution vs. sampling distribution Binomial distributions for sample counts Finding binomial probabilities: tables Binomial mean and standard variation Sample proportions
Purdue University - Main Campus - STAT - 501
Introduction to Inference Section 6.1Estimating with ConfidenceIntroductionDistinguish chance variations from permanent features of a phenomenon:Give SAT test to a SRS of 500 California seniors samplemean = 461 What does it say about the mean SAT sc
Purdue University - Main Campus - STAT - 501
Section 7.1Inference for the mean of a populationChange: Population standard deviation () is now unknown The t distribution One-sample t confidence interval One-sample t test Matched pairs t procedures Robustness of t proceduresThe t distribution:The
Purdue University - Main Campus - STAT - 501
Section 8.1Inference for a Single ProportionRecall: Population ProportionLet p be the proportion of &quot;successes&quot; in a population. A random sample of size n is selected, and X is the count of successes in the sample. Suppose n is small relative to the po
Purdue University - Main Campus - STAT - 501
Chapter 9Two categorical variables. Data Analysis and Inference for Two-Way TablesTopicsImportant change: We switch from quantitative variables to categorical variables describing relations in two-way tables marginal distributions conditional distribut
Purdue University - Main Campus - STAT - 501
Section 10.1Simple Linear RegressionA continuation of Chapter 2Statistical model for linear regression Data for simple linear regression Estimation of the parameters Confidence intervals and significance tests Confidence intervals for mean response vs.
Purdue University - Main Campus - STAT - 501
Section 11.1Multiple Linear Regression (MLR)Topics-MLRExtension of SLR Statistical model Estimation of the parameters and interpretation R-square with MLR Anova Table F-Test and t-testsA continuation of Chapter 10Most things are conceptually similar
Purdue University - Main Campus - STAT - 501
Section 12.1One-Way Analysis of Variance (ANOVA)Inference for One-Way ANOVAComparing means for several groups Format of data An analogy: two sample t-statistic ANOVA hypotheses and model Understanding two types of variation Estimates of population para
Purdue University - Main Campus - STAT - 501
STAT 501Experimental Statistics IPurpose: To explain the essential ideas and concepts of applied statistics, including numericalsummaries, graphing, hypothesis testing, confidence intervals, two-way tables and the Chi-square,regression and ANOVA. Also
Purdue University - Main Campus - STAT - 501
If you find a mistake, please email me ASAP: colvertn@stat.purdue.edu1.a. 89.248b. 0.2215c. (61.3, 88.7)2.a. 0.0479b. No.c. 0.02563.a. 0.9951b. 0.80304.a.b.c.d.N( = 0.7, = 0.0458)0.1379(0.6084, 0.7916)457 guarantees less than 0.01.5.
Purdue University - Main Campus - STAT - 501
Correlation Exampleoptions ls=72;title1 'Gesell Correlation Example';data gesell;infile 'C:\gesell.txt';input name \$ age score;yrs = age/12; /* creating new variable &quot;yrs&quot; whichconverts age in months to age in years */run;symbol value = circle;p
Purdue University - Main Campus - STAT - 501
Exam 1 Review-Summary of topicsChapter 1 Individuals Categorical and Quantitative variables Graphical tools for categorical variables Bar Chart Pie Chart Graphical tools for quantitative variables Stem and leaf plot Histogram Distributions Describe: Shap
Purdue University - Main Campus - STAT - 501
Test of Mean(s):Hypotheses:One SampleH 0:Ha:Two Sample = 0 &gt; 0 &lt; 0 0H 0:Ha:IF you DO know :X 0nTest of Significance:z=Confidence Interval:X z*n(XX 0snt=1IF you do NOT know :Test of Significance:t=Confidence Interval:X t *sn
Purdue University - Main Campus - STAT - 501
Experiments on learning in animals sometimesmeasure how long it takes a mouse to find itsway through a maze. The mean time is 20seconds for one particular maze. A researcherthinks that playing rap music will cause the miceto complete the maze faster
Purdue University - Main Campus - STAT - 501
Getting Started in SASSome general instructions regarding homeworks:Do not use an alternate program(s) to make any of your graphs, for now just make themby hand, in homework 2 we will start using SAS!Occasionally I will give special instructions for s
Purdue University - Main Campus - STAT - 501
1 Sample t-test in SASoptions nodate pageno=1;goptions colors=(none);title1 'One sample t-test in SAS';data one;infile 'C:\gesell.txt';input name \$ age score;run;proc print data=one;run;One sample t-test in SASObs12345678910111213
Purdue University - Main Campus - STAT - 501
Matched Pairs t-test in SASoptions nodate pageno=1;goptions colors=(none);title 'Analysis of Aggressive behaviors - Example 7.7';data moon;input patient aggmoon aggother;aggdiff = aggmoon - aggother;datalines;1 3.330.272 3.670.593 2.670.324
Purdue University - Main Campus - STAT - 501
2 Sample t-test in SASoptions nodate pageno=1;goptions colors=(none);title1 'DRP data - Example 7.14';data drp;input group score @;datalines;1 24 1 43 1 58 1 71 1 43 1 49 1 61 1 441 67 1 49 1 53 1 56 1 59 1 52 1 62 1 541 57 1 33 1 46 1 43 1 572
Purdue University - Main Campus - STAT - 501
Two-Way Tables in SASoptions nodate pageno=1;goptions colors=(none);title 'Age versus College Program - class example';data one;input age \$ program \$ count;datalines;18below2full3618below2part9818below4full7518below4part3718to212full1
Purdue University - Main Campus - STAT - 502
Stat 502 Topic #2 CLG HandoutActivity #1Data concerning statewide average SAT scores was obtained from www.amstat.org. A complete description ofthe data set may be found at http:/www.amstat.org/publications/jse/datasets/sat.txt . Variables in this data
Purdue University - Main Campus - STAT - 502
Topic 8 Handout: One Way Analysis of VarianceLearning Goals for this Activity: (1) Learn the relationships in the ANOVA table and understand theassociated F test; (2) Understand how to get estimates for cell means model (using the output from SAS); (3)
Purdue University - Main Campus - STAT - 502
Topic 10 Handout: ANCOVA &amp; RCBD DesignsLearning Goals for this Activity: (1) Experience in the use of ANCOVA and RCBD Models; (2) Anunderstanding of why such models are worthwhile.10.1Output for Example II (from notes) is given below on pages 1-2. Com
Purdue University - Main Campus - STAT - 502
Topic 11 Handout: Two Way Analysis of VarianceLearning Goals: (1) Learn how to analyze two factors in ANOVA; (2) Understandand be able to properly interpret interactions.11.1Pages 2 and 3 show six possible interaction plots for an analysis of drugeff
Purdue University - Main Campus - STAT - 502
Topic 12 Handout: CARS exampleLearning Goals: (1) Explore the difference between balanced and unbalanced ANOVAdesigns; (2) Further understanding of interactions; (3) Learn about confounding of effectsin ANOVA.The questions are based on the following s
Purdue University - Main Campus - STAT - 502
Topic 13 Handout: Random EffectsLearning Goals: (1) Understand the differences between fixed effects and random effectsmodels; (2) Be able to identify effects as either fixed or random; (3) Be able to utilize EMS(expected mean squares) to determine (a)
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #1Coverage: KKMN Chapters 1-3Name: _SCORE: _ of 30Instructions: Although I do encourage you to work together both in and outside of class, remember thatcollaboration on homework problems should be minimal and everyone should creat
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #1Coverage: KKMN Chapters 1-3Name: _SCORE: _ of 30Instructions: Although I do encourage you to work together both in and outside of class, remember thatcollaboration on homework problems should be minimal and everyone should creat
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #2Coverage: KKMN Chapters 4-7Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!#1.(3 pts) Briefly explain the difference between the following two equations. Do either of theseconstitute a complete statemen
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #3Coverage: KKMN Chapter 8-9Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require any SAS coding.#1.(6 points) KKMN Problem 8.03 as stated. Please note that
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #4Coverage: KKMN Chapter 9Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require SAS coding.#1.(6 points) KKMN Problem 9.02.#2.(4 points) KKMN Problem 9.03
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #5Coverage: KKMN Chapters 10 &amp; 12Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require SAS coding.#1.(7 points) KKMN Problem 10.07. Ignore the questions in
Purdue University - Main Campus - STAT - 502
Topic 1 Basic StatisticsKKMN Chapters 1-31Topic OverviewCourse Syllabus &amp; ScheduleReview: Basic StatisticsTerminology: Being able to CommunicateDistributions: Normal, T, FHypothesis Testing &amp; Confidence IntervalsSignificance Level &amp; Power2Textb
Purdue University - Main Campus - STAT - 502
Topic 2 Simple Linear RegressionKKMN Chapters 4 71OverviewRegression Models; Scatter PlotsEstimation and Inference in SLRSAS GPLOT ProcedureSAS REG ProcedureANOVA Table &amp; Coefficient ofDetermination (R2)2Simple Linear Regression ModelWe take n
Purdue University - Main Campus - STAT - 502
CLG Activity #1Please discuss questions 3.1-3.6from the handout.CLG Activity #1Q1: Research Questions?Is there an effect of smoking on SBP?Is body size associated to SBP?Can any combination of the three variablesbe used to predict SBP?CLG Activit
Purdue University - Main Campus - STAT - 502
Topic 3 Multiple Regression AnalysisRegression on Several PredictorVariables(Chapter 8)1Topic OverviewSystolic Blood Pressure ExampleMultiple Regression ModelsSAS Output for RegressionMulticollinearity2Systolic Blood Pressure DataIn this topic
Purdue University - Main Campus - STAT - 502
Topic 4 CLG Addendum1CLG Activity #1In your groups, please attempt thefirst set of questions. These willinvolve computing various extrasums of squares.2Question 4.1 &amp; 4.2Univariate and bivariate issues that mayaffect modeling include:For HSM, H
Purdue University - Main Campus - STAT - 502
Topic 4 Extra Sums of Squaresand the General Linear TestUsing Partial F Tests in MultipleRegression Analysis(Chapter 9)1Recall: Types of Tests1.ANOVA F Test: Does the group of predictorvariables explain a significant percentage of thevariation i
Purdue University - Main Campus - STAT - 502
CLG ActivityIn CLGs, please attempt Activity#1 from the handout for Topic 5.Note that this activity builds on theone we used for Topic #4.15.1 (a) &amp; (b)2GPA, HSM | HSS , HSE , SATM , SATVr2GPA , HSE | HSMr6.835== 0.061105.65 + 6.8352.48=
Purdue University - Main Campus - STAT - 502
Topic 5 Partial Correlations; Diagnostics &amp;Remedial MeasuresChapters 10 &amp; 141OverviewReview: MLR Tests &amp; Extra SSPartial Correlations Think Extra SS beingused to compute Extra R2Of the variation left to explain.How much isexplained by adding anot
Purdue University - Main Campus - STAT - 502
Topic 6 Model SelectionSelecting the BestRegression Model(Chapters 9 &amp; 16)1OverviewWe already have many of the pieces inplace. Well use those to developalgorithmic procedures.There are some additional statistics that canbe used for comparison of
Purdue University - Main Campus - STAT - 502
Topic 7 Other Regression IssuesReading: Some parts ofChapters 11 and 15OverviewConfounding (Chapter 11)Interaction (Chapter 11)Using Polynomial Terms (Chapter 15)Regression: Primary GoalsWe usually are focused on one of thefollowing goals:Predic
Purdue University - Main Campus - STAT - 502
Topic 8 One-Way ANOVASingle Factor Analysis of VarianceReading: 17.1, 17.2, &amp; 17.5Skim: 12.3, 17.3, 17.41OverviewNote: Entire topic constitutes some reviewas this would be the last thing you coveredin 501. We will cover it perhaps insomewhat more
Purdue University - Main Campus - STAT - 502
Topic 8 One-Way ANOVASingle Factor Analysis of VarianceReading: 17.1, 17.2, &amp; 17.5Skim: 12.3, 17.3, 17.41OverviewNote: Entire topic constitutes some reviewas this would be the last thing you coveredin 501. We will cover it perhaps insomewhat more
Purdue University - Main Campus - STAT - 502
Topic 9 Multiple ComparisonsMultiple Comparisonsof Treatment MeansReading: 17.7-17.81OverviewBrief Review of One-Way ANOVAPairwise Comparisons of Treatment MeansMultiplicity of TestingLinear Combinations &amp; Contrasts ofTreatment Means2Review: O
Purdue University - Main Campus - STAT - 502
Topic 10 ANCOVA &amp; RCBDAnalysis of Covariance (Ch. 13)Randomized Complete BlockDesigns (Ch. 18)1ReviewRecall the idea of confounding. Suppose I want todraw inference about a certain predictor.If meaningfully different interpretations would bemade
Purdue University - Main Campus - STAT - 502
Topic 11 ANOVA IIBalanced Two-Way ANOVA(Chapter 19)1Two Way ANOVAWe are now interested the combined effectsof two factors, A and B, on a response (note:text refers to these as R = rows andC = columns well call them A, B, and laterC for a 3-way AN
Purdue University - Main Campus - STAT - 502
Topic 12 Further Topics in ANOVAUnequal Cell Sizes(Chapter 20)1OverviewWell start with the Learning Activity.More practice in interpreting ANOVA results; anda baby-step into 3-way ANOVA.An illustration of the problems that anunbalanced design wil
Purdue University - Main Campus - STAT - 502
Topic 13 Random EffectsBackground Reading:Parts of Chapters 17 and 191Reading SummarySection 17.1 (particularly page 422)Section 17.6 (pages 438-440)Section 19.7 (pages 538-541)2Random EffectsSo far we have really only dealt with fixedeffects w
Purdue University - Main Campus - STAT - 502
Topic 14 Experimental DesignCrossoverNested FactorsRepeated Measures1OverviewWe will conclude the course by consideringsome different topics that can arise in amulti-way ANOVA, as well as some othermiscellaneous topics.Some of these are discusse
Purdue University - Main Campus - STAT - 506
STAT 506Homework 1You should first go the the website and download the Data folder for the Programming 1course, it is available in a zip file called prg1.zip. I suggest you use your H: drive for storagebut its really up to you. You will need to unzip i
Purdue University - Main Campus - STAT - 506
STAT 506Homework 2For most problems you will still need to access the data in the PRG1 folder. Use the libname statement we learned toload this each time you work on your assignments. You may now call it orion to be consistent with the SASmaterials. Th
Purdue University - Main Campus - STAT - 506
STAT 506Homework 3For most problems you will still need to access the data in the PRG1 folder. Use the libname statement we learned toload this each time you work on your assignments calling the library orion. I tried to bold the parts where I expectyo
Purdue University - Main Campus - STAT - 506
STAT 506Homework 4For most problems you will still need to access the data in the PRG1 folder. Use the libname statement we learned toload this each time you work on your assignments calling the library orion. I tried to bold the parts where I expectyo
Purdue University - Main Campus - STAT - 506
STAT 506Homework 5For most problems you will still need to access the data in the PRG1 folder. Use the libname statement we learned toload this each time you work on your assignments calling the library orion. I tried to bold the parts where I expectyo
Purdue University - Main Campus - STAT - 506
STAT 506Homework 6For most problems you will need to access the data in the PRG2 folder. Use the libname statement we learned to loadthis each time you work on your assignments calling the library orion. I tried to bold the parts where I expect you toa
Purdue University - Main Campus - STAT - 506
STAT 506Homework 7For most problems you will need to access the data in the PRG2 folder. Use the libname statement we learned to loadthis each time you work on your assignments calling the library orion. I tried to bold the parts where I expect you toa
Purdue University - Main Campus - STAT - 506
Chapter 1: Introduction1.1 Course Logistics1.2 Purpose of the Macro Facility1.3 Program Flow1Chapter 1: Introduction1.1 Course Logistics1.2 Purpose of the Macro Facility1.3 Program Flow2Objectives3Explain the naming convention that is used for
Purdue University - Main Campus - STAT - 506
Chapter 2: Macro Variables2.1 Introduction to Macro Variables2.2 Automatic Macro Variables2.3 Macro Variable References2.4 User-Defined Macro Variables2.5 Delimiting Macro Variable References2.6 Macro Functions1Chapter 2: Macro Variables2.1 Intro
Purdue University - Main Campus - STAT - 506
Chapter 3: Macro Definitions3.1 Defining and Calling a Macro3.2 Macro Parameters3.3 Macro Storage (Self-Study)1Chapter 3: Macro Definitions3.1 Defining and Calling a Macro3.2 Macro Parameters3.3 Macro Storage (Self-Study)2Objectives3Define and
Purdue University - Main Campus - STAT - 506
Chapter 4: DATA Step and SQL Interfaces4.1 Creating Macro Variables in the DATA Step4.2 Indirect References to Macro Variables4.3 Retrieving Macro Variables in the DATA Step(Self-Study)4.4 Creating Macro Variables in SQL1Chapter 4: DATA Step and SQ