1. Describe the Form and Direction of the Scatterplot. Warm-Up Does the number of hours you sleep effect your test performance? # hrs sleep 6.5 8.5 9 4 5 6.5 6 3 10 9 8.5 Test % 77 90 92 60 70 75 72 50 98 40 89 1. Describe the Form and Direction of the Scatterplot. Identify any Outliers. Find and Interpret the slope and correlation. Remove Outlier and Find and Interpret the slope and correlation. Name any potential Lurking Variables.

The following is a residual plot based on the regression analysis QUIZ REVIEW - Warm-Up The following is a residual plot based on the regression analysis on the # hours you study and the grade you get on the test. Interpret the slope Interpret the y-intercept What is the actual grade when the student studies for 2 hours? What does a negative residual mean here? Is the Linear model appropriate for the data?

The following is a residual plot based on the regression analysis QUIZ REVIEW - Warm-Up The following is a residual plot based on the regression analysis on the # hours you study and the grade you get on the test. Interpret the slope Interpret the y-intercept What is the actual grade when the student studies for 2 hours? What does a negative residual mean here? Is the Linear model appropriate for the data? For each additional hour you study your predicted grade will increase 15 points on average. b) If you do NOT study (0 hours) you are predicted to score a 50 on avg.

The following is a residual plot based on the regression analysis QUIZ REVIEW - Warm-Up The following is a residual plot based on the regression analysis on the # hours you study and the grade you get on the test. Interpret the slope Interpret the y-intercept What is the actual grade when the student studies for 2 hours? What does a negative residual mean here? Is the Linear model appropriate for the data? c.) Actual Grade base on Resid...

The Difference between Outliers and Influential Points An Outlier is an observation that lies outside the overall pattern of the other observations. An Influential point is an outlier that if removed would significantly change the position of the regression line. Outlier but NOT Influential Outlier and Influential

An Outlier in the x direction, (x-value is far from the mean of all x-values), is called a Leverage Point. It will significantly change the slope and falsely increases the correlation, r.

The Effects of Outliers (again)…. is ALWAYS a central point on the regression line. An Outlier act as “Vertical” Attractor to the line. x y 2 3 4 5 6 8 7 b = 0.60 r = 0.95 2 8 b = 0.18 r = 0.24 REMOVING the Upper Left Outlier = Increase Slope and Increase Correlation

is ALWAYS a central point on the regression line is ALWAYS a central point on the regression line. An Outlier act as “Vertical” Attractor to the line. x y 2 3 4 5 6 8 7 b = 0.60 r = 0.95 8 10 b = 0.88 r = 0.86 REMOVING the Upper Right Outlier = Decrease Slope and Increase Correlation

is ALWAYS a central point on the regression line is ALWAYS a central point on the regression line. An Outlier act as “Vertical” Attractor to the line. x y 2 3 4 5 6 8 7 b = 0.60 r = 0.95 10 1 b = -0.10 r = -0.14 REMOVING the Lower Right Outlier = Increase Slope and Increase Correlation

is ALWAYS a central point on the regression line is ALWAYS a central point on the regression line. An Outlier act as “Vertical” Attractor to the line. x y 2 3 4 5 6 8 7 b = 0.60 r = 0.95 2 0 b = 0.88 r = 0.87 REMOVING the Lower Left Outlier = Decrease Slope and Increase Correlation

is ALWAYS a central point on the regression line is ALWAYS a central point on the regression line. An Outlier act as “Vertical” Attractor to the line. x y 2 3 4 5 6 8 7 b = 0.60 r = 0.95 5 9 b = 0.60 r = 0.87 REMOVING the Center Outlier = Slope stays the same and Increase Correlation

HW Page 215: 11(omit part 1), 13 2: NO 3: Weaker – Leverage 4: Stay the same b) 2: Yes 3: Weaker – Leverage 4: Increase c) 2: Yes 3: Stronger – Outlier 4: Increase d) 2: Yes 3: Stronger – Outlier 4: Stays the same

What will happen to the SLOPE and to the CORRELATION COEFFICIENT if the point is removed?

Chapter 9 (cont.) Outliers, Leverage, and Influence Points The following scatterplot shows that something was awry in Palm Beach County, Florida, during the 2000 presidential election…

Outliers, Leverage, and Influence (cont.) The red line shows the effects that one unusual point can have on a regression: