Bivariate Analysis

6-1 Simple Linear Regression Analysis, p. 502
- define, and use in context, the following key terms: simple regression; linear regression; equation of a regression model; population parameters of the simple linear regression model, A and B; random error term; estimated values of A and B, namely a and B, respectively; estimated regression model; predicted value of y; scatter diagram
  - Simple regression
  - Linear regression
  - Equation of a regression model
  - Estimates of A and B
- construct a scatter diagram based on sample data.
  - Scatter diagram
- find the estimated regression model (equation), given sample data.
  - Simple linear regression model
  - Assumptions of the regression model
- interpret the values of a and b based on the estimated regression model.
  - Interpretation of a and b
- plot the regression line
  - Least squares regression line
- compute the error of prediction, e, for a given value of x.
  - Cautions in using regression
6-2 Standard Deviation of Random Errors and the Coefficient of Determination, p. 517
- define, and use in context, the following key terms: standard deviation of errors; coefficient of determination
  - Standard deviation of error.
    - Degrees of freedom for a simple linear regression model
    - standard deviation of errors
- compute the standard deviation of errors.
- compute the coefficient of determination, and interpret your answer
  - Coefficient of determination
- Total sum of squares (SST)
- Regression sum of squares (SSR)
6-3 Inferences About the Slope of the Simple Linear Regression Model, B, p. 522
- define, and use in context, the term "sampling distribution of b."
  - Sampling distribution of b
- construct a confidence interval for B.
  - Estimation of B
- conduct tests of hypotheses about B when H0 is B=0.
  - Hypothesis testing about B
- ~~Using the p-Value to Make a Decision, pp. 526–527~~
6-4 Linear Correlation, p. 527
- define, and use in context, the following key terms: linear correlation; positive linear correlation, negative linear correlation, and zero linear correlation; perfect positive linear correlation; perfect negative linear correlation
  - Linear correlation coefficient
  - Value of the correlation coefficient
- compute the linear correlation coefficient, given population or sample data, and interpret your answer.
  - conduct tests of hypotheses about the population linear correlation coefficient.
  - Hypothesis testing about the linear correlation coefficient
  - Test statistic for r
- ~~Using the p-Value to Make a Decision, p. 532~~
6-5 Applying Correlation and Regression, p. 532
- define, and use in context, the term "prediction interval"
- demonstrate an understanding of the nature of the linear relation b/w 2 variables by
  - computing and interpreting the correlation coefficient and the coefficient of determination
  - testing hypotheses relating to the population correlation coefficient
  - determining the least squares regression equation and interpreting the coefficients a and b
  - plotting the scatter diagram and the regression line
  - constructing confidence intervals for B
  - testing hypotheses related to B
  - computing a point estimate of the dependent variable, given a value for the independent variable
- use the regression model to construct confidence intervals for estimating the mean value of y, given a value of x.
- Using the regression model
  - Using the regression model for estimating the mean value of y
    confidence interval for $μ_{y | x}$
  - Using the regression model for predicting a particular value of y
  - Prediction interval for $y^{p}$
- use the regression model to construct confidence intervals for predicting a particular value of y, given a value of x.
- Regression analysis - a complete example
- ~~Using the p-Value to Make a Decision for the hypothesis test on B, p. 537~~
- ~~The hypothesis test on the linear correlation coefficient, p. 538~~