Presentation on theme: "Least-Squares Regression Section 3.3. Correlation measures the strength and direction of a linear relationship between two variables. How do we summarize."— Presentation transcript:
Least-Squares Regression A method for finding a line that summarizes the relationship between two variables, but only in a specific setting.
Regression Line “Best-fit Line” A straight line that descirbes how a response variable y changes as an explanatory variable x changes. Predict y from x. Requires that we have an explanatory variable and a response variable.
Extrapolation Suppose that we have data on a child’s growth between 3 and 8 years of age. The least-squares regression line gives us the equation, where x represents the age of the child in years, and will be the predicted height in inches. What if you wanted to predict the height of a 25 year old girl? Would this equation be appropriate to use? NO!
Extrapolation Extrapolation is the use of a regression line for prediction far outside the domain of values of the explanatory variable x that you used to obtain the line or curve. Such predictions are often not accurate. That’s over 7’ 9” tall!