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x 3 5 6 8 8 11 y 21 25 24 30 41 50 8 a. Use tables and formulas to determine the linear regression equation for the data set. b. Verify that the regression line has a smaller sum of squared error than lines A and B from Exercise (33)

x 3 5 6 8 8 11 y 21 25 24 30 41 50 8 a. Use tables and formulas to determine the linear regression equation for the data set. b. Verify that the regression line has a smaller sum of squared error than lines A and B from Exercise (33)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 78E
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**Table 4.24** | \( x \) | 3 | 5 | 6 | 8 | 11 | |--------|---|---|---|---|----| | \( y \) | 21 | 25 | 24 | 30 | 41 | ### Problem Statement **a.** Use tables and formulas to determine the linear regression equation for the data set. **b.** Verify that the regression line has a smaller sum of squared error than lines A and B from Exercise (33).
Transcribed Image Text:**Table 4.24** | \( x \) | 3 | 5 | 6 | 8 | 11 | |--------|---|---|---|---|----| | \( y \) | 21 | 25 | 24 | 30 | 41 | ### Problem Statement **a.** Use tables and formulas to determine the linear regression equation for the data set. **b.** Verify that the regression line has a smaller sum of squared error than lines A and B from Exercise (33).
### Data from Exercise #33 #### Table Data | Line A: y = 6 + 4x | Line B: y = 7 + 3.5x | |---------------------|---------------------| | x | 3 | 5 | 6 | 8 | 11 | | y | 21 | 25 | 24 | 30 | 41 | 50 | #### Scatterplot of y vs x The scatterplot depicts the relationship between variable x and variable y. Individual data points are marked with red dots. Two linear regression lines are shown: - **Line A**: Represented by the equation \( y = 6 + 4x \), this line is labeled as "A" on the graph. - **Line B**: Represented by the equation \( y = 7 + 3.5x \), this line is labeled as "B" on the graph. **Axes:** - The x-axis ranges from 3 to 11, consistent with the values provided in the table. - The y-axis ranges from 20 to 50, encompassing the calculated y-values from both Line A and Line B. The scatterplot reveals how the given linear models (Line A and Line B) fit the data points: - For Line A, the y-values for the given x-values are: 18, 26, 30, 38, and 50. - For Line B, the y-values for the given x-values are: 17.5, 24.5, 28, 36, and 47.5. Each dot's position reflects the corresponding y-value for each x as calculated by the specified equations, highlighting the relationship and differences between the two lines.
Transcribed Image Text:### Data from Exercise #33 #### Table Data | Line A: y = 6 + 4x | Line B: y = 7 + 3.5x | |---------------------|---------------------| | x | 3 | 5 | 6 | 8 | 11 | | y | 21 | 25 | 24 | 30 | 41 | 50 | #### Scatterplot of y vs x The scatterplot depicts the relationship between variable x and variable y. Individual data points are marked with red dots. Two linear regression lines are shown: - **Line A**: Represented by the equation \( y = 6 + 4x \), this line is labeled as "A" on the graph. - **Line B**: Represented by the equation \( y = 7 + 3.5x \), this line is labeled as "B" on the graph. **Axes:** - The x-axis ranges from 3 to 11, consistent with the values provided in the table. - The y-axis ranges from 20 to 50, encompassing the calculated y-values from both Line A and Line B. The scatterplot reveals how the given linear models (Line A and Line B) fit the data points: - For Line A, the y-values for the given x-values are: 18, 26, 30, 38, and 50. - For Line B, the y-values for the given x-values are: 17.5, 24.5, 28, 36, and 47.5. Each dot's position reflects the corresponding y-value for each x as calculated by the specified equations, highlighting the relationship and differences between the two lines.
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