9.6: Vocabulary (Chapter 9)
- Page ID
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter 9 Vocabulary
- Bivariate Data
- Data that includes two quantitative variables measured for each individual in a study. Often used to examine relationships between variables.
- Scatterplot
- A graph that displays pairs of numerical data as points on a coordinate plane. Each point represents an individual’s value for two variables (x and y).
- Direction of Association
- A description of how one variable tends to change as the other changes. Associations can be positive, negative, or have no clear direction.
- Positive Association
- When values of one variable tend to increase as the values of the other variable also increase. The pattern typically slopes upward from left to right.
- Negative Association
- When values of one variable increase as the other decreases. The pattern typically slopes downward from left to right.
- Correlation (r)
- A numerical measure between –1 and 1 that describes the strength and direction of a linear relationship between two variables. A value close to ±1 indicates a strong linear relationship.
- Correlation Coefficient (r)
- Another name for the correlation measure. It quantifies linear association but does not imply causation.
- Least-Squares Regression Line (LSRL)
- The line that best fits a scatterplot and minimizes the sum of the squared residuals. It models the linear relationship and can be used for prediction.
- Regression Equation
- The formula of the form \( \hat{y} = a + bx \) where \( \hat{y} \) is the predicted value, \( a \) is the intercept, and \( b \) is the slope.
- Slope
- In a regression line, the slope tells how much the predicted value of \( y \) changes for each one-unit increase in \( x \). It represents the rate of change.
- Intercept
- The y-value predicted when \( x = 0 \) in a regression model. It may or may not be meaningful depending on the context and data range.
- Residual
- The difference between an actual data value and the value predicted by a regression model. Residual = actual – predicted.
- Interpolation
- Using a regression model to predict a value within the range of the observed data.
- Extrapolation
- Using a regression model to predict a value outside the range of the observed data. It can be risky because the relationship may not hold beyond the data range.
- Causation
- The idea that one variable has a direct effect on another. Causation implies a change in one variable produces a change in the other. It requires evidence beyond just statistical association.
- Correlation Does Not Imply Causation
- A reminder that even strong relationships between variables do not prove one causes the other. Alternate explanations or lurking variables may be involved.