Regression in biostatistics example. This model explains 58% of the variation in home prices.

These rules limit the form to just one type: Dependent variable = constant + parameter * IV + … + parameter * IV. To know more about Correlation and regression formulas, the difference between correlation and regression with examples, you can visit us at BYJU’S – The Learning App. Systolic blood pressure, weight (ounces) and age (days) are measured in 100 infants. The authors reported that they had limited ability to conclude This chapter describes multiple linear regression, a statistical approach used to describe the simultaneous associations of several variables with one continuous outcome. where X is the independent variable and plotted along the x-axis. The only difference between simple linear regression and multiple regression is in the number of predictors (“x” variables) used in the regression. In this section we discuss correlation analysis which is a technique used to quantify the associations between two continuous variables. Regression analysis is a Jan 24, 2022 · Abstract. Print. Important steps in using this approach include estimation and inference, variable selection in model building, and assessing model fit. If height were the only determinant of iv. Know how to obtain the estimates b 0 and b 1 from Minitab's In this example, the sample mean of the 14 observations is 9. Aimed specifically at the health sciences, Biostatistics by Example Using SAS Studio, provides an introduction to SAS Studio tasks. One of the measurement variables is the dependent ( Y) variable. What's included. This course is part of Biostatistics in Public Health Specialization. Module 1 • 4 hours to complete. Agricultural scientists often use linear regression to measure the effect of fertilizer and water on crop yields. Manuscript Sections. 2 suggest a weak, negative association. e. Using the regression equation y x = 2. 6+1. Hadi, Samprit Chatterjee. Financial aid available. Interpret the results of a correlation analysis. Research. H0 : b1 = 0 vs. Upon completion of this lesson, you should be able to: Distinguish between a deterministic relationship and a statistical relationship. In summary, while both Statistics and Biostatistics involve the use of statistical methods, the main difference lies in the application of these methods. Logistic regression is a statistical method for modeling the dependence of a categorical (binomial) outcome variable on one or more categorical and continuous predictor variables (Bewick et al 2005). Oct 7, 2021 · Introduction. ⁡. Jun 28, 2024 · Biostatistics is crucial in conducting research and clinical trials, as it helps to ensure the validity and reliability of the results. where X is plotted on the x-axis and Y is plotted on the y-axis. The special cases of regression with Apr 1, 2014 · Logistic regression: In situations in which the response of interest is dichotomous (binary) rather than continuous, linear regression cannot be used to explore the nature of the relationship. m is the slope, which tells us the predicted increase Use multiple regression when you have three or more measurement variables. 01165 + 0. For the statistical of the slope, b1, we generally treat the test as a two-tailed test of the null hypothesis that the regression slope is equal to zero. We explain why traditional regression adjustment fails and discuss the methods of g-computation, sequential stratification, marginal structural models, and structural nested models. ( μ i) = β 0 + β 1 X i, which means we’d really like to plot μi μ i as a function of the explanatory variable. 2,3 Rather than modeling a linear relationship between the independent variable (X) and the probability of the outcome (Figure A), which is unnatural since it would allow predicted probabilities outside the range of 0–1, it assumes a linear (straight line) relationship with the logit (the natural logarithm of the odds) of the Nov 1, 2016 · Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation (y = a + bx), such that given the value of one variable the other may C regression. A regression equation is used in stats to find out what relationship, if any, exists between sets of data. A linear regression line equation is written in the form of: Y = a + bX. As will be discussed in Chapters 8 and 9, there are problems with interpreting any regression models, yet compared to the other statistical learning machines we eventually discuss, logistic regression is far easier to interpret. Use multiple logistic models to understand how risk of kyphosis (curvature of the spine) depends on several predictor variables. regression. Department of Biostatistics Vanderbilt University School of Medicine. 8057 or 80. Briefly speaking, statistics plays a key role in all phases of a research project starting from the design stage and continuing through the monitoring, data collection, data analysis and interpretation of the This site provides detailed information about performing common statistical tests and procedures in Excel including t-tests, ANOVA, repeated measure ANOVA, Correlation, Simple and Multiple Linear Regression, calculating confidence intervals and other descriptive statistics. The result is the impact of each variable on the odds ratio of the observed event of interest. a. Study Table 13. PRACTICE PROBLEMS FOR SIMPLE LINEAR REGRESSION (Some are new & Some from Old exams; last 4 are from 2010 Midterm) Problem 1: The Pearson Correlation Coefficient (r) between two variables X and Y can be expressed in several equivalent forms; one of which is n i y i x i s y y s x x n r X Y 1 _ _ ( )( ) 1 ( , ) Multiple regression analysis is almost the same as simple linear regression. A correlation close to zero suggests no linear association between two continuous variables. Simple Regression Analysis in Public Health. Day #02: Review 2: Simple Correlation and Regression. Jul 31, 2023 · d) Regression analysis. 2 b = 2. Multiple Regression Line Formula: y= a +b1x1 +b2x2 + b3x3 +…+ btxt + u. In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables In their example (p 297), RR=3. This tutorial covers many facets of regression analysis including selecting the correct type of regression analysis, specifying the best model, interpreting the results, assessing the fit of the model, generating predictions, and checking the assumptions. Biostatistics (also known as biometry) is the application of statistical methods to biology. For example, if you measure a child’s height every year you might find that they grow about 3 inches a year. Table 13. 57%. HA : b1 ≠ 0. Few applications of biostatistics are summarized below. Find the mean values and coefficient of correlation between X and Y. A value of R 2 close to 1 means that the regression “explains” nearly all of the variation in the response Dec 7, 2019 · B. Objectives. Example: Multiple Linear Regression by Hand. The two regression lines were found to be 4X–5Y+33=0 and 20X–9Y–107=0 . Some common inferential statistical tests include t-tests, ANOVA, chi-square, correlation and regression. Application of statistical methods in biomedical research began more than 150 years ago. Examples are drawn from various biomedical and health-related studies. t. Continuous and categorical explanatory variables are considered. Recall the slope-intercept form of a line, y = mx + b. 26721 × age. In this example, if an individual was 70 inches tall, we would predict his weight to be: Weight = 80 + 2 x (70) = 220 lbs. The rest of the variables are the independent ( X) variables; you think they may have an effect on the dependent variable. #drcjtank#pharmaplanet#biostatistics2. 9 suggests a strong, positive association between two variables, whereas a correlation of r = -0. 43. In our example above, R 2 = 0. The variability or dispersion concerns how spread out the values are. Step 1: Calculate X 1 2, X 2 2, X 1 Apr 17, 2024 · The regression formula in statistics is a method to estimate or calculate the relation between two or more variables. Choose the option "This Collection" under 4 days ago · Biostatistics with R provides a straightforward introduction on how to analyse data from the wide field of biological research, including nature protection and global change monitoring. Abstract. May 31, 2016 · We could use the equation to predict weight if we knew an individual's height. The interpretation of the slope is that the average FEV increases 0. 1 years, larger than the sample standard deviation of 2. π(1- π) Biostatistics has applications in all the branches of life sciences. 12. 22 languages available. Technical Condition 1, Line: The Poisson model implies that the log of the mean will be a linear function of the explanatory variable: ln(μi) = β0 +β1Xi, ln. ¯y) ∑n 1 (x−¯. What is the purpose of the Central Limit Theorem in statistics? a) To determine the sample size needed for a study b) To describe the shape of a normal distribution c) To estimate population parameters from sample statistics d) To calculate the variance of a sample. Some important formulas used in inferential statistics for regression analysis are as follows: Regression Coefficients: The straight line equation is given as y = α α + βx β x, where α α and β β are regression coefficients. Review: slope-intercept form of a line. Unfortunately, there are no textbooks which could appropriately fulfill the requirements of the Biostatistics course at the undergraduate level for Health officer and Medical students. If b xy is positive, then b yx is also positive and vice versa. Starting at just $116. 6811 which is more than 1. For many studies, the researchers have more data than they know how to handle. 15. That trend (growing three inches a year) can be modeled with a regression May 9, 2024 · A parameter multiplied by an independent variable (IV) Then, you build the linear regression formula by adding the terms together. My tutorial helps you go through the regression content in a systematic and logical order. Logistic regression has probably been underutilized in clinical investigations of personality because of its relatively recent development (dictated by the need for computer programs to obtain maximum likelihood estimates), and the fact that use has been largely confined to the fields of biostatistics, epidemiology, and economics Its Basic Biostatistics presents a multidisciplinary survey of biostatics methods, each illustrated with hands-on examples. What is the “Regression” of Y on X ? — Average Y at each value of X. Methods range from the elementary, including descriptive statistics, study design, statistical interference, categorical variables, evaluation of diagnostic tests, comparison of means, linear regression, and logistic regression. Interpret the effects of length of stay and employee salary on per capita health care expenditures. Day #03: Review 3: Experimental Designs. The correlation coefficient r is a dimensionless number ranging from -1 to +1. LINEAR REGRESSION. 7 years for the original seven observations. , N, where is Biostatistics refers to the application of statistical techniques to biologic data collected prospectively and/or retrospectively. Interpret the intercept b 0 and slope b 1 of an estimated regression equation. There are two main types: simple linear regression, which involves two variables, and multiple regression, which involves more than two variables. Introduction . Jan 14, 2021 · Logistic regression is actually an extension of linear regression. Day #04: Correlation Analysis. Biostatistics. 26721 for each one year increase in age (in the observed age range). Learn how to solve basic statistical problems with Ron Cody's easy-to-follow style using the point-and-click SAS Studio tasks. Topics include: the simple regression model, estimation of regression parameters-least squares estimation, maximum likelihood estimation, residuals and their properties, expectation and variance of the parameter estimators, student t-test in testing hypothesis about the parameters, confidence interval of the parameters, mean : BIOSTATISTICS REGRESSION, 2011 . In the blue equation, m = 1 and b = 5. Jan 6, 2016 · Logistic regression is just one such type of model; in this case, the function f (・) is. They might fit a multiple linear regression model using Definition of biostatistics Statistics — the science of collecting, describing, analyzing, and interpreting data, so that inferences (conclusions about a population based on data from merely a sample) can be made with quantifiable certainty. However, despite the name linear regression, it can model One criterion for a good model is that the coefficients in the model, the intercept and the slope (s) are all statistically significant. Keywords: binomial distribution, Hosmer–Lemeshow test, likelihood, likelihood ratio test, logit function, maximum Correlation and regression analysis are applied to data to define and quantify the relationship between two variables. From the data find out the regression equation and draw a regression line on the graph paper. The logistic regression model applies a logistic or sigmoid function to the linear combination of the independent variables. It is the predicted value of y when x = 0. For example, a researcher studying cancer outcomes may have both gene expression and copy number data for a set of patients. Feb 20, 2020 · Multiple linear regression formula. = the y-intercept (value of y when all other parameters are set to 0) = the regression coefficient () of the first independent variable () (a. We can find the probability of the dependent variable from this odds ratio. The document discusses regression analysis and its key concepts. 5 years for the original seven observations. 47 This lesson reviews correlation and linear regression. The objective of a study is to understand the factors that are associated with systolic blood pressure in infants. The procedure is quite similar to multiple linear regression, with the exception that the response variable is binomial. Indeed, the rapidly developing statistical methodology and its recent advances in regression modeling do not seem to be adequately reflected in The geometric mean between the two regression coefficients is equal to the correlation coefficient. At the end of this lesson, you will be able to: Define correlation. Use logistic regression to classify subjects and assess the quality of a classification rule with its sensitivity, specificity and ROC curve. Digital Evaluation Copy. Drawing upon your education in introductory biostatistics, the theory of epidemiology, the scientific method, etc – see how many Whereas when data were generated from a perfect additive Cox proportional hazards regression model the inclusion of the interaction between the two covariates resulted in only 2% estimated bias in main effect regression coefficients estimates, but did not alter the main findings of no significant interactions. the effect that increasing the value of the independent variable May 19, 2020 · Linear Regression Real Life Example #3. Nov 17, 2014 · The problem of combining data from multiple assays is an important topic in modern biostatistics. A practice quiz is provided to test your knowledge before completing the graded quiz. bootstrap. E-Book. Section 4 illustrates some practical applications of quantile regression in biostatistics. There is a free resource pack and example workbooks available to download. Author. 48x the actual values of dependent variable can be worked out. The first three chapters cover basic concepts of Statistics focusing on PubH 7405: Biostatistics Regression (Fall 2019) Day #01: Review 1: Basics of Statistical Inferences; plus Course Information , Syllabus , and Presentations . e. For example, we might predict weight W = 71. Some content may not be translated. The sample standard deviation of the 14 observations is 3. The slope of the line is b, and a is the intercept (the value of y when x = 0). Each additional term can be viewed as another predictor in the regression equation: \(y=\beta_0 + \beta_1x + \beta_2x^2 + \dots + \beta_px^p + \varepsilon\) This allows the fit of more flexible models representing the association between the outcome and some continuous predictors. (1). Midterm exam -censored regression regression, in case-control prediction. One equation for R 2 is given by. ¯x)(y−¯. Model In the current presentation, we consider the data in the form ( ,)T Xy i i, for i = 1, 2, . Understand the concept of the least squares criterion. 9 years, smaller than the sample mean of 10. 9 videos 2 readings 2 quizzes. validation. Frank Harrell. BiBTeX EndNote RefMan. Additionally, examples and applications will be examined. ISBN: 978-1-119-83089-4 October 2023480 Pages. Learning objectives. The purpose of a multiple regression is to find an equation that best predicts the Least-Squares Line (Regression Line or Line of Best Fit) 0 1 0 1 11 22 2 0 22 01 note that is the y-intercept aˆ nd is the slope ( )( ) where or ( )( ) ( )( ) ( )( ) where or ( )( ) y x y b bx b n xy x y s b br nx x s and y x x xy b b y bx nx x = + ∑ −∑ ∑ == ∑ −∑ ∑ ∑ −∑ ∑ = = − ∑ −∑ 0 0 00 2 /2 2 2 1 1 11 /2 2 2 Regression analysis can be thought of as being sort of like the flip side of correlation. The conclusions from her tables helped to change the practices The Poisson is different than the binomial, Bin(n, π), which takes on numbers only up to some n, and leads to a proportion (out of n). For example, we might want to quantify the association between body mass index and systolic blood pressure, or between hours of exercise per week and percent body fat. A value of -1 signifies a perfect negative, or Jun 5, 2012 · For example, individual genes or clinical findings can be assigned protective or risk values expressed as log odds. The exponential beta value in the logistic regression output denotes the odds ratio of the dependent variable. Chapter 4: Reading Data from Text Files . There is a big confusion between subscript i and n in the formula for mean and standard deviation (p 71-72). It specifically helps determine how much a dependent variable (Y) is affected by one or more independent variables (X), where: Y – is the dependent variable. It is important to note that there may be a non-linear association between two 2 we discuss quantile regression model, and section 3 focuses on the inference related to model parameter(s). Jan 13, 2005 · This review introduces logistic regression, which is a method for modelling the dependence of a binary response variable on one or more explanatory variables. Linear, GLM, and Cox regression models are explained with a 2 days ago · A linear regression line equation is written as-. For instance, in the red equation, m = 1 and. Ø For the design of experiments. May 21, 2018 · Biostatistics is just a tool – those who conduct clinical trials should make sure that it is used properly and that the results are aligned with critical thinking. Nov 18, 2020 · This tutorial explains how to perform multiple linear regression by hand. M 1pm-2:50pm Jul 9, 2020 · There are 3 main types of descriptive statistics: The distribution concerns the frequency of each value. 1 below briefly and then continue. The authors cover t-tests, ANOVA and 11. For example, with 10 groups we Inferential stats allow you to assess whether patterns in your sample are likely to be present in your population. Feb 15, 2014 · Abstract. The author has attempted a mathematical exposition but has not succeeded. This formula is linear in the parameters. X is an independent variable and Y is the dependent variable. Linear regression is a toolkit for developing linear models of cause and effect between a ratio scale data type, response or dependent variable, often labeled “ Y ,” and one or more ratio scale data type, predictor or independent variables, X. To identify and measure causal relationships, you need a very specific Mar 25, 2024 · Logistic Regression: Logistic regression is used when the dependent variable is binary or categorical. If you are interested in these topics, SPH offers. Basics of Biostatistics. The central tendency concerns the averages of the values. - An example uses home size and price data from 10 houses to generate a linear regression equation predicting that price increases by around $110 for each additional square foot. value of y when x=0. We firmly believe that this lecture note will fill that gap. The book includes many biological and health-related problem Biostatistics. Oct 29, 2015 · A common misinterpretation of linear regression is the 'regression fallacy'. Furthermore, because of the simple form of the Poisson 2. This new book provides a unified, in-depth, readable introduction to the multipredictor regression methods most widely used in biostatistics: linear models for continuous outcomes, logistic models for binary outcomes, the Cox model for right-censored survival times, repeated-measures models for longitudinal and hierarchical outcomes, and generalized linear models for counts and other outcomes. For example: (x 1, Y 1). The equations of two lines of regression obtained in a correlation analysis are the following 2X=8–3Y and 2Y=5–X . Jan 17, 2023 · Example 2: Logistic Regression Models Biostatisticians often use logistic regression models to predict whether or not individuals or animals will have a particular binary outcome (yes or no). 6 kg for a larger than average height H = 175 cm and then predict height H Sep 29, 2013 · Regression analysis outputs include coefficients, residuals, and measures of fit like the R-squared value. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation ( y = a + bx ), such that given the value of one variable the other may be predicted. Affiliation. My main goal in that class is to teach biology students how to choose the appropriate statistical test for a particular experiment, then apply that test and Mean of Y = Pr(Y=1) = π 0≤ π ≤1, and fitted values may fall outside of (0,1). However, that’s a minor problem. Introduction. In this simple linear regression, we are examining the impact of one independent variable on the outcome. Determine when to use a linear regression analysis. 1947-2022. 47 . Cox proportional Cox proportional hazards and hazard Adaptive Regression No clas (Memorial Day) design in HIV prevention in statistical Overview. Prerequisites: S&DS 542 and BIS 623 or their equivalents. The book is centred around traditional statistical approaches, focusing on those prevailing in research publications. k. Here, b is the slope of the line and a is the intercept, i. f (E [Y]) = log [ y/ (1 - y) ]. β = ∑n 1(x−¯. Request Digital Evaluation Copy. Harvard affiliates with an ID number and PIN can get free download of dissertations, both Harvard and other, on the Digital Access to Scholarship at Harvard site via DASH . Describe the Pearson correlation coefficient and the Spearman correlation coefficient. 26721 × (8) = 2. Regression analysis can be determined using tools such as R or SPSS to find a relationship between independent variables and outcome. One of the early pioneers, Florence Nightingale, the icon of nursing, worked during the Crimean war of the 1850s to improve the methods of constructing mortality tables. Ø Every result (data) in the research need to be statistically validated. For instance, for an 8 year old we can use the equation to estimate that the average FEV = 0. Enroll for Free. Jan 26, 2023 · prediction. But the Poisson is similar to the binomial in that it can be show that the Poisson is the limiting distribution of a Binomial for large n and small π. However, if we have more groups, this becomes quite complicated. Like ANOVA, linear regression is a special case of the general linear model. Dec 6, 2006 · These programs typically have one to three courses that focus on biostatistics methods, and Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models is designed to be the primary biostatistics textbook for the second or third of these courses. Statistics is a broader field that is used in various For example, using multivariable logistic regression to analyze data from a nested case-control study revealed that some carotenoids were inversely associated with breast cancer suggesting that plasma levels of α- or β-carotene may play a role in reducing breast cancer risk . A good model fit has a high R 2 value. 95. Regression analysis is used to understand the relationship between two or more variables and make predictions. For example, scientists might use different amounts of fertilizer and water on different fields and see how it affects crop yield. Although regression models play a central role in the analysis of medical research projects, there still exist many misconceptions on various aspects of modeling leading to faulty analyses. Logistic Regression Model: p = 1 / (1 + e^- (β0 + β1X1 + β2X2 + … + βnXn)) In the formula: p represents the Critically evaluate a multiple linear regression analysis to ensure that substantive findings are appropriate given the data. A multiple linear regression is performed to predict blood pressure (mm Hg) from age and weight. Free B Pharmacy Handwritten Notes for Biostatistics And Research Methodology Unit 2 - 8th Semester Jan 8, 2024 · Simple logistic regression assumes that the observations are independent; in other words, that one observation does not affect another. Correlation analysis is used to estimate the strength of a relationship between two variables. Jul 2, 2024 · Regression is a statistical measure used in finance, investing and other disciplines that attempts to determine the strength of the relationship between one dependent variable (usually denoted by Example: pets and stress We are interested in testing H 0: P = F = N against the alternative that at least one mean is di erent from the others. Day #05: Estimation of Parameters. Regression Analysis By Example Using R, 6th Edition. Ø Research is incomplete without the statistics. . Starts Jul 16. . For example if the outcome is mortality, the two outcomes possible are alive or dead. A regression analysis of measurements of a dependent variable Y on an independent variable X produces a statistically significant association between X and Y. b is the y-intercept, or where the line crosses the y-axis. Within this module, an overview of multiple regression will be provided. 2. Suppose we have the following dataset with one response variable y and two predictor variables X 1 and X 2: Use the following steps to fit a multiple linear regression model to this dataset. There is Poisson regression (count data), Gamma regression (outcome strictly greater than 0), Multinomial regression (multiple categorical outcomes), and many, many more. Biostatistics — that portion of statistics that is most relevant to the biological sciences. The examples I cite are illustrative of some of the errors in the book. One way to do this would be to use t-tests on all possible pairs of tests (here there are just three). The estimated regression equation is that average FEV = 0. Using data of the given example the straight line is drawn but the point of interception to y-axis is lacking and, therefore, precise nature of the Topics studied in biostatistics are too numerous to list (for example multivariate regression, analysis of covariance, linear discriminant analysis, principal component analysis, and so forth; therefore, a sample that reflects the kind of tools that are used and most prevalent techniques will be given. Y is the dependent variable and plotted along the y-axis. 42. In the Komodo dragon example, if all the eggs at \(30^{\circ}C\) were laid by one mother, and all the eggs at \(32^{\circ}C\) were laid by a different mother, that would make the observations non-independent. May 19, 2022 · The application of simple linear regression analysis was discussed. However, in practice, we hardly go beyond the degree 3. For example, researchers can measure a variety of variables including weight, height, age, etc. Instructor: John McGready, PhD, MS. 1 Prepregnancy Weights of Mothers and Birthweights of their Infants. Y = a + bX. This model explains 58% of the variation in home prices. Inferential statistics alone do not prove causation. In general, the method of least squares is applied to obtain the equation of the regression line. X – is the independent (explanatory) variable. 00. After reading this The regression analysis will then indicate the best set of predictors, from those included, and one can use these to predict the outcome for new cases. It has to do with finding the equation for the kind of straight lines you were just looking at. Obtain the value of the regression coefficients and correlation coefficient. Finally, section 5 concludes. The book includes many biological and health-related problem sets and is fully compatible with SAS University Edition. This is an example statistical plan for project proposals where the goal is to develop a biostatistical model for prediction, and to do external or strong internal validation of the model. Click on "By Collections" in the left hand menu under Statistics, and select "FAS Theses and Dissertations" in the list. It includes the design of biological experiments, the analysis of data from those experiments and the interpretation of the results. Starting at just $144. so they can fit a logistic regression model that tells Dec 23, 2017 · Biostatistics: Linear regression and correlation. a Regression || Biostatistics and Research Methodology || BP801TT ||Join my Telegram Channel and Download Study Materia Welcome to the third edition of the Handbook of Biological Statistics! This online textbook evolved from a set of notes for my Biological Data Analysis class at the University of Delaware. Simple regression analysis uses a single x variable for each dependent “y” variable. The logistic function may be used to transform a sigmoidal curve to a more or less straight For example, a correlation of r = 0. We expand our discussion of logistic regression here. The formula for a multiple linear regression is: = the predicted value of the dependent variable. Logistic regression is used to obtain odds ratio in the presence of more than one explanatory variable. The Variance (around the regression line) is not constant (a model violation that we learn in diagnostics); variance is function of the Mean π of Y (which is a function of predictors): σ2 =. R 2, the square of the simple product moment correlation r, can take on values between 0 and 1 (0% to 100%). Final exam (8:30am – 10:30am) be communicated a tentative may schedule of. Taught in English. ¯. Ali S. You can apply these to assess only one variable at a time, in univariate analysis, or to compare two or more, in Use linear regression or correlation when you want to know whether one measurement variable is associated with another measurement variable; you want to measure the strength of the association ( r2 ); or you want an equation that describes the relationship and can be used to predict unknown values. be iq tr oc zb jp lk vz sm cx