Lesson 4 (N) How wil the line fits the data - Copy

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May 1, 2024

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Chapter 3 Describing Relationships Lesson 4 How well the line fits the data 1. Determining if a linear model is appropriate: Residual Plots; 2. The Standard Deviation of the Residuals ; 3. The coefficient of Determination . 1. Determining if a linear model is appropriate: Residual plots help us assess whether or not a linear model is appropriate. Example 1: A scatterplot shows the relationship between the number of hours studied the night before a test and score for the test.

The line seems to be a good fit for this relationship. The residuals look randomly and evenly scattered around the line. We can’t see any obvious curved pattern in the residual plot. Example 2: The least-squares regression line clearly doesn’t fit this association very well!

This U-shaped pattern in the residual plot indicates that the linear form of our model doesn’t match the form of the association. A curved model might be better in this case. https://savi-cdn.macmillantech.com/brightcove/index.html? videoId=5731634971001 To determine whether the regression model is appropriate, look at the residual plot. ● If there is no curved pattern in the residual plot and the residuals are evenly scattered above and below the line, the regression model is appropriate. ● If there is a curved pattern in the residual plot, consider using a regression model with a different form. Example 3: Is a linear model appropriate to describe the relationship between the weight (in carats) and price (in dollars) of diamonds with excellent cuts? Interpretation: The linear model relating price to carat weight is not appropriate because there is a U- shaped pattern in the residual plot. 2. The Standard Deviation of the Residuals:

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