{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture-18-Simple Linear Regression

# Lecture-18-Simple Linear Regression - LECTURE 18 Simple...

This preview shows pages 1–3. Sign up to view the full content.

LECTURE 18 Simple Linear Regression (Part 2): The Coefficient of Determination This lecture covers material on measuring the goodness of fit for the estimated regression equation using the Coefficient of Determination. Microsoft Excel is used for some applications. Read: Chapter 12, Section 12.3. In Lecture 19, we learnt how to compute the estimated linear regression equation from sample data by using the least squares method. We now want to know how good is the fit between this estimated equation values ( ŷ i ) and the actual observation ( y i ). The measure used for determining the goodness of fit is the Coefficient of Determination. To compute the Coefficient of Determination we need to compute three values: 1. Sum of Squares Due to Error (SSE) 2. Total Sum of Squares (SST) 3. Sum of Squares Due to Regression (SSR) ___________________________________________________________ We will use the example in Lecture 18 shown below to illustrate our computations . A company launches a new product and conducts an extensive advertising campaign for four months with advertising expenditure inceasing every month. It wants to develop an equation showing how sales is related to its expenditure on advertising. The data is shown in the table below. Advertising Expenditure (\$ 1000s): 1 2 3 4 Product Sales (in 1000 units): 2 4 4 6 1

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

View Full Document
Sum of Squares Due to Error (SSE ) In Lecture 15, we had seen that the Least Squares Method minimizes the sum of the squares of the differences between the observed values of y i and the corresponding estimated values of ŷ i . Therefore the objective of Least Squares method is: Min Σ ( y i - ŷ i ) 2 The difference ( y i - ŷ i ) is also known as the ith residual and represents the error in using ŷ i
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern