Stat 226 - Section 2.1 - Recall Exploratory Data Analysis...

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Chapter 2 Examining Relationships Chapter 2 1 Recall - Exploratory Data Analysis Use some statistical tools to describe some of the main features of the dataset. This process is known as exploratory data analysis . Begin by examining each variable by itself (Chapter 1). Then look at relationships between variables (Chapter 2). Begin by visualizing important features with graphs. Then focus on specifics by using numerical summaries. What graphics and numerical summaries are available for relationships between variables? Chapter 2 2 Relationships To study a relationship between two variables, we measure both variables on the same individuals. We want to understand how a change in one variable corresponds to a change in another variable. Since there will always be variability across individuals, we are interested in overall tendencies, understanding that there will be individual exceptions. Chapter 2 3 Two-Variable Relationships What two variables are being examined? Is there a gender gap in the preference of candidates for governor of Iowa (Jim Nussle or Chet Culver)? Is there a difference in the distribution of annual salaries for different levels of education (High School, Bachelor’s, Professional Degree)? Chapter 2 4 Two-Variable Relationships What two variables are being examined? How does tumor growth in laboratory animals change as the dose of a drug increases? Does the time required to complete a computer programming task change based on the number of years of experience of the programmer? Chapter 2 5 Variable Types From the examples, we can see that relationships can involve any combination of categorical and quantitative variables. It is often natural to view one variable as having an effect on, explaining, or influencing the other variable. This is especially true when we control the value of one variable. We can decide what dose of drug to give to laboratory animals. Chapter 2 6
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Variable Types A response variable measures an outcome or a result of a study. Another name is a dependent variable . The variable in a one-variable study is a response variable. It may be a variable that we wish to predict . An explanatory variable is a variable that explains or influences a response variable. Another name is a independent variable . This is the variable that we could have control over. Chapter 2 7 Explanatory and Response Variables What are the explanatory and response variables? Is there a gender gap in the preference of candidates for governor of Iowa (Jim Nussle or Chet Culver)? Is there a difference in the distribution of annual salaries for different levels of education (High School, Bachelor’s, Professional Degree)?
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