12. Regression

In the context of regression analysis, what is a residual, and what does it indicate when a residual is positive? (A residual is typically defined as $e=y-\hat{y}$, where $y$ is the observed value and $\hat{y}$ is the predicted value.)

In the context of regression analysis, what is a residual, and what does it indicate when a residual is positive? (A residual is typically defined as $e=y-\hat{y}$, where $y$ is the observed value and $\hat{y}$ is the predicted value.)

In residuals analysis, what should the residual plot look like if the regression line fits the data well?

In the context of residuals analysis, what does a residual value of $-0.8$ indicate about a data point relative to the line of best fit?

Which of the following patterns in a residual plot indicates that the line of best fit is appropriate for the data?

Which of the following residual plots suggest that a linear regression model is appropriate?

1. What is a residual? Explain when a residual is positive, negative, and zero.

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Error of Estimate Find the standard error of estimate Se and interpret the results."

"Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 11-20, use the data to (b) find the standard error of estimate s_e and interpret the result.

12. [APPLET] Median and Mean Hourly Wages The table shows the median and mean hourly wages (in dollars) in 10 states in a recent year. The equation of the regression line is y = 1.208x + 1.495. (Source: U.S. Census Bureau)

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"Graphical Analysis In Exercises 1–3, use the figure.

1. Describe the total variation about a regression line in words and in symbols."

"Graphical Analysis In Exercises 1–3, use the figure.

2. Describe the explained variation about a regression line in words and in symbols."

"Graphical Analysis In Exercises 1–3, use the figure.

Describe the unexplained variation about a regression line in words and in symbols."

[DATA] The following data represent the height (inches) of boys between the ages of 2 and 10 years.

b. Compute the standard error of the estimate, Sₑ.