Chapter 14. Descriptive Methods in Regression and Correlation. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 1
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1 Chapter 14 Descriptive Methods in Regression and Correlation Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 1
2 Section 14.1 Linear Equations with One Independent Variable Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 2
3 Definition 14.1 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 3
4 Key Fact 14.1 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 4
5 Section 14.2 The Regression Equation Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 5
6 Definition 14.2 Scatterplot A scatterplot is a graph of data from two quantitative variables of a population. In a scatterplot, we use a horizontal axis for the observations of one variable and a vertical axis for the observations of the other variable. Each pair of observation is then plotted as a point. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 6
7 Table 14.2 Age and price data for a sample of 11 Orions Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 7
8 Figure 14.7 Scatterplot for the age and price data of Orions from Table 14.2 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 8
9 Table 14.3 & Figure 14.8 Three data points Scatterplot for the data points in Table 14.3 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 9
10 Figure 14.9 Two possible lines to fit the data points in Table 14.3 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 10
11 Table 14.4 Determining how well the data points in Table 14.3 are fit by (a) Line A and (b) Line B Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 11
12 Key Fact 14.2 & Definition 14.3 Least-Squares Criterion The least-squares criterion is that the line that best fits a set of data points is the one having the smallest possible sum of squared errors. Regression Line and Regression Equation Regression line: The line that best fits a set of data points according to the least-squares criterion. Regression equation: The equation of the regression line. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 12
13 Definition 14.4 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 13
14 Formula 14.1 (see previous page) Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 14
15 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 15
16 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 16
17 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 17
18 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 18
19 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 19
20 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 20
21 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 21
22 Table 14.6 Table for computing the regression equation for the Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 22
23 Figure Regression line and data points for Orion data Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 23
24 Figure Interpretation of the slope of the fitted regression line: The estimated mean reduction in price is $2026 for each year increase in age of the car. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 24
25 Definition 14.5 Response Variable and Predictor Variable Response variable: The variable to be measured or observed. Predictor variable: A variable used to predict or explain the values of the response variable. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 25
26 Figure Extrapolation in the Orion example Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 26
27 Figure Regression lines with and without the influential observation removed Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 27
28 Key Fact 14.3 Criterion for Finding a Regression Line Before finding a regression line for a set of data points, draw a scatterplot. If the data points do not appear to be scattered about a line, do not determine a regression line. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 28
29 Section 14.3 The Coefficient of Determination Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 29
30 Definition 14.6 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 30
31 Definition 14.7 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 31
32 Table 14.7 Table for finding the three sums of squares Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 32
33 Key Fact 14.4 Regression Identity The total sum of squares equals the regression sum of squares plus the error sum of squares: SST = SSR + SSE. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 33
34 Formula 14.2 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 34
35 Formula 14.2 Note by the above definition of SSR, we see that, SST = SS yyyy and SSR = SS xxxx 2 SS xxxx Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 35
36 Table 14.8 Table for finding SST and SSR for the Orion data by using the computing formulas Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 36
37 Table 14.8 Table for finding SST and SSR for the Orion data by using the computing formulas Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 37
38 Table 14.8 Table for finding SST and SSR for the Orion data by using the computing formulas Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 38
39 Table 14.8 Table for finding SST and SSR for the Orion data by using the computing formulas Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 39
40 Table 14.8 Table for finding SST and SSR for the Orion data by using the computing formulas Coefficient of determination Or, 85.3% Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 40
41 Table 14.8 Table for finding SST and SSR for the Orion data by using the computing formulas Interpretation: 85.3% of the variability in price is explained by the regression of price on Age. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 41
42 Table 14.8 Table for finding SST and SSR for the Orion data by using the computing formulas Interpretation: 85.3% of the variability in price is explained by the regression of price on Age. Regression/Prediction Equation Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 42
43 Section 14.4 Linear Correlation Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 43
44 Definition 14.8 & Formula 14.3 Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 44
45 Figure Various degrees of linear correlation Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 45
46 Key Fact 14.5 Relationship between the Correlation Coefficient and the Coefficient of Determination The coefficient of determination equals the square of the linear correlation coefficient. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 46
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