4.2

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Scatter Diagrams Example: The average salary S (in millions of dollars) for a major corporation from 1998 through 2004 is shown in the table. (a) Draw a scatter diagram of the data treating the year as the independent variable. (b) Describe what happens as the years increase. Continued. Year Salary, S

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Scatter Diagrams Example continued: Year Salary, S Salary (in millions of dollars) y x Year (b) It appears that the salary increases as the years increase. The pattern of the data is linear. (a)

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Types of Relationships

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Fitting Data Example: Using the data in Table 4 (next slide), (a)Select two points and find a linear model that describes the relation between the points. (b)Graph the line on the scatter diagram obtained in Example 6(a). (c)Use the linear model found in part (a) to predict the number of runs scored by a team whose on-base percentage is 34.6%. (d)Interpret the slope. Does it make sense to interpret the y-intercept? Continued.

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Fitting Data Continued.

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Fitting Data Example continued: (a) Select two points (32.2, 706) and (36.6, 968) and find the slope. Continued. Use the point-slope form with m = 59.55, x 1 = 32.2, and y 1 = 706.

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Fitting Data Example continued: (b) The figure shows the scatter diagram with the graph of the line found in part (a). We obtain the graph of the line by drawing the line through the two points selected in part (a). Continued.

Sullivan, III & Struve, Elementary and Intermediate Algebra Copyright © 2010 Pearson Education, Inc. Fitting Data Example continued: Round to the nearest whole number. We predict that a team whose on base percentage is 34.6% will score 849 runs. (c) Evaluate f (34.6) = 59.55(34.6) – = (d) The slope of the linear function is This means that if the on-bas percentage increases by 1, then the number of runs scored will increase by about 60 runs.They- intercept, represents the runs scored when the on-base percentage is 0. Since negative runs scored does not make sense and we do not have any observations near zero, it does not make sense to interpret the y-intercept.