Cpt 13 Example Problems (1) - Chapter 13 Simple Linear...

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Chapter 13 – Simple Linear RegressionRegression analysisenables you to develop a model to predict the values of a numerical variable, based on the value of other variables. In regression analysis, the variable you wish to predict is called the dependent variable. The variables used to make the prediction are called independent variables.Regression analysis also allows you to:-Identify the type of relationship that exists between a dependent and an independent variable.-Quantify the effect that changes in the independent variable have on the dependent variable.-Identify any unusual observations.This chapter discusses simple linear regression, where a single numerical independent variable, X, is used to predict the numerical dependent variable, Y.Ex. = Chapters 14 and 15 discuss multiple regression, which uses several independent variables, X’s, to predict a numerical dependent variable, Y.Ex. =
Section 13.1 – Types of Regression Models In Section 2.5, you used a scatter plot to examine the relationship between an X variable on the horizontal axis and a Y variable on the vertical axis. The relationship between 2 variables can take many forms, from simple to extremely complicated. The simplest is a linear relationship.Simple Linear Regression Model:Yi= β0+ β1Xi+ εiβ0= β1= Section 13.2 – Determining the Simple Linear Regression Equation Let’s suppose we can assume that a straight line provides a useful model ofa relationship. Now we need to determine the specific equation of that straight line that is the bestfit to these data.The Least-Squares Method:The data we have is always only from a sample. We can use this data to estimate the form of the simple linear regression equation. This straight line is often referred to as the prediction equation.
Simple Linear Regression Equation: The Prediction LineYi= b0+ b1XiThe least-squares method minimizes the sum of the squared differences between the actual values (Yi) and the predicted values (Yi) using the simple linear regression equation.When predicting Y for a given value of X, you can interpolatewithin this relevant range of the X values, but you should not extrapolatebeyond the range of X values.Ex. = The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. A random sample of 12 stores is selected, with the following results:StoreShelf Space(feet)WeeklySales ($)151600252200351400410190051024006102600715230081527009152800102026001120290012203100

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