Lecture 6

# Lecture 6 - 6.2142857*4 =-10.7142858 Thus the regression...

This preview shows pages 1–12. Sign up to view the full content.

Relationships can be deceiving An outlier is defined to be any value that is more than 1.5*IQR beyond the closest quartile. A value is an outlier if either 1) the value is greater than Q 3 +(1.5*IQR) 2) the value is less than Q 1 -(1.5*IQR) Ex. What is the possible outlier? X: 2 5 7 9 10 11 55 Q 1 = P 25 =(n*k)th # Q 3 = P 75 =(n*k)th #

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

View Full Document
IQR = A value is an outlier if either 1) the value is greater than 2) the value is less than
How does an outlier effect the correlation? X: 1 2 3 4 5 6 7 Y: 2 5 7 9 10 11 55 x y 7 6 5 4 3 2 1 60 50 40 30 20 10 0 Scatterplot of y vs x

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

View Full Document
Find the correlation X Y X 2 Y 2 XY 1 2 1 4 2 2 5 4 25 10 3 7 9 49 21 4 9 16 81 36 5 10 25 100 50 6 11 36 121 66 7 55 49 3025 385 x= y= x 2 = y 2 xy

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

View Full Document
Now drop the outlier we found earlier and find the correlation. X Y X 2 Y 2 XY 1 2 1 4 2 2 5 4 25 10 3 7 9 49 21 4 9 16 81 36 5 10 25 100 50 6 11 36 121 66 x= y x 2 y 2 xy

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

View Full Document
How does an outlier effect the correlation? Using the same values and the Sum of Squares form the previous examples X: 1 2 3 4 5 6 7 Y: 2 5 7 9 10 11 55 For all the original 7 pairs of points X = x n = 28/7 = 4 Y = y n = 99/7 = 14.142857 b = SSxy/SSxx = 174/28 = 6.2142857 a = Y - b* X = 14.142857 –

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.2142857*4 = -10.7142858 Thus, the regression line for the original 7 pairs is ˆ y = 6.2142857*x - 10.7142858 x y 7 6 5 4 3 2 1 60 50 40 30 20 10 Scatterplot of y vs x Now drop the outlier we found earlier and find the correlation. So, we are only working with 6 pairs of numbers. X = x n ∑ = 21/6 = 3.5 Y = y n ∑ = 44/6 = 7.333333333 b = SSxy/SSxx = 31/17.5 = 1.771428571 a = Y- b* X = 7.33333333– 1.771428571*3.5 = 1.13333333 Thus, the regression line for the 6 pairs after the outlier is dropped. ˆ y = 1.771428571*x + 1.133333333 x_1 y_1 6 5 4 3 2 1 12 10 8 6 4 2 Scatterplot of y_1 vs x_1 Now look at the two regression lines superimposed on the same graph X-Data Y-Data 7 6 5 4 3 2 1 60 50 40 30 20 10 Variable y * x y_1 * x_1 Scatterplot of y vs x, y_1 vs x_1 The outlier pulls the regression line towards it....
View Full 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