Statistics and Data
Coordinate Algebra Name: _____________________
4.2.3 Residuals Date: _____________________
Introduction
The fit of a linear function to a set of data can be assessed by analyzing__________________. A residual is the vertical distance between an observed data value and an estimated data value on a line of best fit. Representing residuals on a___________________________ provides a visual representation of the residuals for a set of data. A residual plot contains the points: (x, residual for x). A random residual plot, with both positive and negative residual values, indicates that the line is a good fit for the data. If the residual plot follows a pattern, such as a U-shape, the line is likely not a good fit for the data.
Key Concepts * A residual is the distance between an observed data point and an estimated data value on a line of best fit. For the observed data point (x, y) and the estimated data value on a line of best fit (x, y0), the residual is y – y0. Day | Height in centimeters | 1 | 3 | 2 | 5.1 | 3 | 7.2 | 4 | 8.8 | 5 | 10.5 | 6 | 12.5 | 7 | 14 | 8 | 15.9 | 9 | 17.3 | 10 | 18.9 | * A residual plot is a plot of each x-value and its corresponding residual. For the observed data point (x, y) and the estimated data value on a line of best fit (x, y0), the point on a residual plot is (x, y – y0).
Guided Practice
Example 1
Pablo’s science class is growing plants. He recorded the height of his plant each day for 10 days. The plant’s height, in centimeters, over that time is listed in the table to the right.
Pablo determines that the function y = 1.73x + 1.87 is a good fit for the data. How close is his estimate to the actual data? Approximately how much does the plant grow each day?
1. Create a scatter plot of the data.
2. Draw the line of best fit through two of the data points.
x | y = 1.73x + 1.87 | 1 | y = 1.73(1) + 1.87 = | 2 | y =
4.2.3 Residuals Date: _____________________
Introduction
The fit of a linear function to a set of data can be assessed by analyzing__________________. A residual is the vertical distance between an observed data value and an estimated data value on a line of best fit. Representing residuals on a___________________________ provides a visual representation of the residuals for a set of data. A residual plot contains the points: (x, residual for x). A random residual plot, with both positive and negative residual values, indicates that the line is a good fit for the data. If the residual plot follows a pattern, such as a U-shape, the line is likely not a good fit for the data.
Key Concepts * A residual is the distance between an observed data point and an estimated data value on a line of best fit. For the observed data point (x, y) and the estimated data value on a line of best fit (x, y0), the residual is y – y0. Day | Height in centimeters | 1 | 3 | 2 | 5.1 | 3 | 7.2 | 4 | 8.8 | 5 | 10.5 | 6 | 12.5 | 7 | 14 | 8 | 15.9 | 9 | 17.3 | 10 | 18.9 | * A residual plot is a plot of each x-value and its corresponding residual. For the observed data point (x, y) and the estimated data value on a line of best fit (x, y0), the point on a residual plot is (x, y – y0).
Guided Practice
Example 1
Pablo’s science class is growing plants. He recorded the height of his plant each day for 10 days. The plant’s height, in centimeters, over that time is listed in the table to the right.
Pablo determines that the function y = 1.73x + 1.87 is a good fit for the data. How close is his estimate to the actual data? Approximately how much does the plant grow each day?
1. Create a scatter plot of the data.
2. Draw the line of best fit through two of the data points.
x | y = 1.73x + 1.87 | 1 | y = 1.73(1) + 1.87 = | 2 | y =