Chapter 13 - Linear regression and correlation, after studying this chapter you will be able to: Identify a relationship between variables on a scatter diagram, measure and interpret a degree of relationship by a coefficient of correlation, conduct a test of hypothesis about the coefficient of correlation in a population,.and other contents. | Chapter 13 Linear Regression and Correlation GOALS Understand and interpret the terms dependent and independent variable. Calculate and interpret the coefficient of correlation, the coefficient of determination, and the standard error of estimate. Conduct a test of hypothesis to determine whether the coefficient of correlation in the population is zero. Calculate the least squares regression line. Construct and interpret confidence and prediction intervals for the dependent variable. Regression Analysis - Introduction Recall in Chapter 4 the idea of showing the relationship between two variables with a scatter diagram was introduced. In that case we showed that, as the age of the buyer increased, the amount spent for the vehicle also increased. In this chapter we carry this idea further. Numerical measures to express the strength of relationship between two variables are developed. In addition, an equation is used to express the relationship between variables, allowing us to . | Chapter 13 Linear Regression and Correlation GOALS Understand and interpret the terms dependent and independent variable. Calculate and interpret the coefficient of correlation, the coefficient of determination, and the standard error of estimate. Conduct a test of hypothesis to determine whether the coefficient of correlation in the population is zero. Calculate the least squares regression line. Construct and interpret confidence and prediction intervals for the dependent variable. Regression Analysis - Introduction Recall in Chapter 4 the idea of showing the relationship between two variables with a scatter diagram was introduced. In that case we showed that, as the age of the buyer increased, the amount spent for the vehicle also increased. In this chapter we carry this idea further. Numerical measures to express the strength of relationship between two variables are developed. In addition, an equation is used to express the relationship between variables, allowing us to estimate one variable on the basis of another. EXAMPLES Is there a relationship between the amount Healthtex spends per month on advertising and its sales in the month? Can we base an estimate of the cost to heat a home in January on the number of square feet in the home? Is there a relationship between the miles per gallon achieved by large pickup trucks and the size of the engine? Is there a relationship between the number of hours that students studied for an exam and the score earned? Correlation Analysis is the study of the relationship between variables. It is also defined as group of techniques to measure the association between two variables. Scatter Diagram is a chart that portrays the relationship between the two variables. It is the usual first step in correlations analysis The Dependent Variable is the variable being predicted or estimated. The Independent Variable provides the basis for estimation. It is the predictor variable. Scatter Diagram Example The sales manager
