Overview[ edit ] In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics such as "all persons living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population an operation called census. This may be organized by governmental statistical institutes.
All Modules Introduction to Correlation and Regression Analysis In this section we will first discuss correlation analysis, which is used to quantify the association between two continuous variables e. Regression analysis is a related technique to assess the relationship between an outcome variable and one or more risk factors or confounding variables.
The outcome variable is also called the response or dependent variable and the risk factors and confounders are called the predictors, or explanatory or independent variables.
In regression analysis, the dependent variable is denoted "y" and the independent variables are denoted by "x".
The term "predictor" can be misleading if it is interpreted as the ability to predict even beyond the limits of the data. Also, the term "explanatory variable" might give an impression of a causal effect in a situation in which inferences should be limited to identifying associations.
The terms "independent" and "dependent" variable are less subject to these interpretations as they do not strongly imply cause and effect. Correlation Analysis In correlation analysis, we estimate a sample correlation coefficient, more specifically the Pearson Product Moment correlation coefficient.
The correlation between two variables can be positive i.
The sign of the correlation coefficient indicates the direction of the association. The magnitude of the correlation coefficient indicates the strength of the association.
A correlation close to zero suggests no linear association between two continuous variables. You say that the correlation coefficient is a measure of the "strength of association", but if you think about it, isn't the slope a better measure of association? We use risk ratios and odds ratios to quantify the strength of association, i.
The analogous quantity in correlation is the slope, i. And "r" or perhaps better R-squared is a measure of how much of the variability in the dependent variable can be accounted for by differences in the independent variable. The analogous measure for a dichotomous variable and a dichotomous outcome would be the attributable proportion, i.
Therefore, it is always important to evaluate the data carefully before computing a correlation coefficient. Graphical displays are particularly useful to explore associations between variables.
The figure below shows four hypothetical scenarios in which one continuous variable is plotted along the X-axis and the other along the Y-axis.
Scenario 3 might depict the lack of association r approximately 0 between the extent of media exposure in adolescence and age at which adolescents initiate sexual activity.
Example - Correlation of Gestational Age and Birth Weight A small study is conducted involving 17 infants to investigate the association between gestational age at birth, measured in weeks, and birth weight, measured in grams. We wish to estimate the association between gestational age and infant birth weight.
In this example, birth weight is the dependent variable and gestational age is the independent variable. The data are displayed in a scatter diagram in the figure below. Each point represents an x,y pair in this case the gestational age, measured in weeks, and the birth weight, measured in grams.
Note that the independent variable is on the horizontal axis or X-axisand the dependent variable is on the vertical axis or Y-axis. The scatter plot shows a positive or direct association between gestational age and birth weight.
Infants with shorter gestational ages are more likely to be born with lower weights and infants with longer gestational ages are more likely to be born with higher weights. The formula for the sample correlation coefficient is where Cov x,y is the covariance of x and y defined as are the sample variances of x and y, defined as The variances of x and y measure the variability of the x scores and y scores around their respective sample meansconsidered separately.
The covariance measures the variability of the x,y pairs around the mean of x and mean of y, considered simultaneously. To compute the sample correlation coefficient, we need to compute the variance of gestational age, the variance of birth weight and also the covariance of gestational age and birth weight.
We first summarize the gestational age data. The mean gestational age is: To compute the variance of gestational age, we need to sum the squared deviations or differences between each observed gestational age and the mean gestational age.
The computations are summarized below.
The variance of gestational age is:Introduction. This page is designed for those who have a basic knowledge of elementary statistics and need a short introduction to time-series analysis. Job Descriptions Introduction This module will help you understand the purpose and components of essential functions job descriptions s and provide you with the tools to develop them.
Job descriptions clarify what an employee is responsible for and what is expected of them. Preparing a thorough, complete job description is a critical first step.
Introduction to Correlation and Regression Analysis. In this section we will first discuss correlation analysis, which is used to quantify the association between two continuous variables (e.g., between an independent and a dependent variable or between two independent variables).
1 The Probability Distribution of Daily Rainfall in the United States Lars S. Hanson 1 and Richard Vogel 2 1 GKY & Associates, Lafayette Center Dr., #, Chantilly, VA , (ph) and Dept.
of Civil and Environmental. A Short Introduction to Eviews Note You are responsible to get familiar with Eviews as soon as possible. All homeworks monthly, weekly, daily) within the same work ﬁle page. 3 Creating a workﬁle To create a new workﬁle click File > New > Workﬁle. If you have quarterly data One common task in time series analysis is the creation.
Introduction to Time Series Regression Time series data are data collected on the same observational unit at multiple time periods Aggregate consumption and GDP for a country (for example, 20 years of quarterly observations = 80 observations) Yen/$, pound/$ and Euro/$ exchange rates (daily data for 1 year = observations).