12. Regression

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

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

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

In the context of residuals analysis, what does the independent observation assumption imply when examining a residuals plot?

In the context of residuals analysis, what does it mean if a data point has a residual value of $1.3$ with respect to the line of best fit for a data set?

In the context of regression analysis, what is a residual, and what does it indicate when a residual is positive ($e$ > $0$)?

Given a data point with observed value $y$ and predicted value $y^{^}$ at $x=1$, which point would appear on the residual plot of the data?

In the context of regression analysis, what is a residual ($e$), and what does it indicate when a residual is positive ($e>\; 0$)?

Which of the following residual plots would indicate that a least squares regression line ($LSRL$) is an appropriate model for the data?

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

According to the plot of $residuals$ versus $fittedvalues$, which of the following patterns would most likely indicate that the assumptions of $linearregression$ are violated?

Which residual plot indicates that the model is a good fit for the data?

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

In the context of regression analysis, what is a residual, and under what condition is a residual considered positive?

In the context of regression analysis, what is a residual, and what does it indicate when a residual is positive? $e=y-\hat{y}$