{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 14 Simple Linear Regression

# Chapter 14 Simple Linear Regression - Chapter 14 Simple...

This preview shows pages 1–2. Sign up to view the full content.

Chapter 14 – Simple Linear Regression - Regression analysis can be used to develop an equation showing how two variables are related - The variable being predicted is the dependent variable , and the variable being used to predict that value of the dependent variable is the independent variable (y denotes the dependent variable and x denotes the independent variable) - The simplest type of regression analysis, simple linear regression , involves one independent variable and one dependent variable where the relationship between the two is approximated by a straight line (regression analysis involving two or more independent variables is multiple regression analysis) Simple Linear Regression Model Regression Model and Regression Equation - The equation that describes how y is related to x and an error term is called the regression model ( Equation 14.1 p. 555 ): y = β 0 + β 1 x + ε - β 0 and β 1 are the parameters of the model, and ε is a random variable referred to as the error term, which accounts for the variability in y that cannot be explained by the linear relationship between x and y - The equation that describes how the expected value of y, denoted E(y), is related to x is the regression equation ( Equation 14.2 p. 556 ): E(y) = β 0 + β 1 x - The graph of this equation is a straight line, with β 0 the y-intercept of the regression line, β 1 the slope, and E(y) the mean or expected value of y for a given value of x Estimated Regression Equation - If the population parameters were known, Equation 14.2 can be used to compute the mean value of y for a given value of x; however the parameter values are not known, and sample statistics are used to estimate the population parameters - Substituting the values of the sample statistics b0 and b1 for β 0 and β 1 in the regression equation, the estimated regression equation ( Equation 14.3 p. 557 ) is obtained: ŷ = b o + b 1 x - The graph of this equation is the estimated regression line, where b 0 is the y-intercept and b 1 is the slope (using the least squares method, these values can be computed in the estimated regression equation) - In general, ŷ is the point estimator of E(y), the mean value of y for a given value of x (known simply as the estimated value of y , since it provides both a point estimate of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Chapter 14 Simple Linear Regression - Chapter 14 Simple...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online