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
Using the regression model for predicting a particular value of y
Prediction interval for
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