Chapter_10_11

# Chapter_10_11 - Chapters 10 and 11 Terminology Measurement...

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Terminology: - Measurement or Quantitative Variables: variables that involve measurement or counting: e.g. number of pages in a book (count), number of students in class (count), height (measured), weight (measured), exam score (measured). - Deterministic Relationship: One variable is directly related to another. For example, if we know your height in inches we can easily convert the height to centimeters by multiplying by 2.54 - Statistical Relationship: a relationship where a natural variability exists. Consider the first exam scores and mean quiz score. Although there is a relationship between the performance on both of these variables, students having the same mean quiz average did not achieve the same exam score. For instance, 4 students have a quiz average of 92.22 but had the following exam scores: 73.3, 86.7, 86.7, and 96.7 - Linear Relationship and Regression: if there exists a statistical relationship where one measurement variable reacts in a linear manner with a change in the second measurement variable then we can employ what is called in statistics regression methods to explore and explain this linear relationship. For instance, if we can show that a linear relationship exists between mean quiz scores and exam scores then we can use regression methods to explain and predict one variable based on the other. - Response, Outcome, Dependent variable versus Explanatory, Independent, Predictor variable: in regression the response or outcome or dependent variable is the variable we are interested in predicting or explaining using a second variable called the explanatory or independent or predictor variable. E.g. we want to predict exam scores (response/outcome) based on mean quiz scores (predictor/explanatory); explain the variation in weight (response/outcome) using height (predictor/explanatory) Determining Linear Relationship - Scatterplot: this is a plot of points for the combinations of the observations of the response and predictor variables putting the response on the Y or vertical axis and the predictor on the X or horizontal axis. - For the scatterplot below what can you see? i. Does the plot indicate any relationship? ii. If yes, is it linear? iii. If linear what direction? - From this plot you can see that there appears to be a linear relationship that is positive. That is, as Quiz Average increases so does Exam score. A negative relationship evolves when as the predictor variable increases the response decreases. (e.g. consider driving speed and travel time: the faster you drive (i.e. speed increases) travel time decreases. 1

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Chapter_10_11 - Chapters 10 and 11 Terminology Measurement...

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