Lecture-17-Summer2010

# Lecture-17-Summer2010 - LECTURE 17 Correlation and Simple...

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LECTURE 17 Correlation and Simple Linear Regression (Part 1) This lecture describes modeling the relationship between two variables using simple linear regression, and using the least squares method. Microsoft Excel is used for some applications. Read: Chapter 12, Section 12.1 and 12.2. We often use statistics to investigate how two variables are related. In this chapter we will consider the relationship between quantitative variables. For example, a company may want to know if sales are increasing with increasing expenditure on advertising. In this case the two variables are sales and advertising expenditure . There are two aspects to this relationship: (1) Are sales associated with advertising expenditures? (2) What is the mathematical relationship between sales and advertising expenditures? To answer the above questions we can take a sample with the data showing advertising expenditures and associated sales levels. We can plot the data in a scatter diagram. If the points in the scatter diagram tend to cluster about a straight line, there exists a linear association (or linear relationship or linear correlation) between the two variables. The closer the points are to the straight line the stronger the degree of linear association. Scatter diagrams (or scatter plots) visually display the relationship between two variables: are they related as a straight line, as a curve, or is there no relationship between the two? 1

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We can solve the problem using Excel. IN THE EXCEL SPREADSHEET INPUT THE DATA TABLE IN TWO COLUMNS A B 1 X Y 2 1 2 3 2 4 4 3 4 5 4 6 Scatter Diagram: SELECT THE TWO COLUMNS CLICK ON CHART WIZARD IN TOOL BAR AND PLACE IT ON A CELL WHERE YOU WANT TO SHOW THE GRAPH. STEP 1: RANGE IS A2 - B5. CLICK ON NEXT STEP 2: SELECT (XY) SCATTER DIAGRAM. CLICK ON NEXT STEP 3: SELECT AN APPROPRIATE FORMAT FOR GRAPH - SAY 3. CLICK ON NEXT STEP 4: DATA SERIES IN COLUMNS. CLICK ON NEXT STEP 5: LABELS - "ADVT EXP" FOR x AND "SALES" FOR y . CLICK ON FINISH THE SCATTER DIAGRAM IS DISPLAYED IN EXCEL. The diagram shows that the points are clustered in a linear fashion.
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## This note was uploaded on 09/21/2011 for the course OM 210 taught by Professor Singer during the Summer '08 term at George Mason.

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Lecture-17-Summer2010 - LECTURE 17 Correlation and Simple...

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