residuals and residual plots most likely a linear regression will not fit the data perfectly. the...

Residuals and Residual Plots Most likely a linear regression will not fit the data perfectly. The residual (e) for each data point is the ________________________ from the data point to the regression line. It is the error in __________________. To find the residual (e) of a data point, take the ________________________ and subtract the __________________________ (y value from the linear regression). The sum of the residuals is equal to _____. That is, Σ e = Residuals can be plotted on a scatterplot called a ____________________________. The horizontal x-axis is the same ________________________ as the original graph. The vertical y-axis is now the ________________________. LOOKING AT RESIDUAL PLOTS: When a set of data has a linear pattern, its residual plot will have a ____________________________. If a set of data does not have a linear pattern, its residual plot will _______________________, but rather, will have a _____________. HOW TO USE RESIDUAL PLOTS: ˆ (e y y) distanc e predict ion observed y value predicted value zer o Residual Plot x value residua l random pattern NOT be random shap e Use Linear Regression DO NOT USE Linear Regression Consider some other type of ˆ y

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Residuals and Residual Plots

Most likely a linear regression will not fit the data perfectly.

The residual (e) for each data point is the ________________________

from the data point to the regression line. It is the error in __________________.

To find the residual (e) of a data point, take the ________________________

and subtract the __________________________ (y value from the linear regression).

The sum of the residuals is equal to _____. That is, Σ e =

Residuals can be plotted on a scatterplot called a ____________________________. The horizontal x-axis is the same ________________________ as the original graph.

The vertical y-axis is now the ________________________.

LOOKING AT RESIDUAL PLOTS:

When a set of data has a linear pattern, its

residual plot will have a ____________________________.

If a set of data does not have a linear pattern, its

residual plot will _______________________, but rather,

will have a _____________.

HOW TO USE RESIDUAL PLOTS:

If the residual plot is RANDOM:If the residual plot is NON-random:

ˆ( e y y )

distance predicti

onobserved y valuepredicted

valuezero

Residual Plotx valueresidual

random pattern

NOT be randomsha

Use Linear RegressionDO NOT USE Linear

RegressionConsider some other type of regression.

Page 2: Residuals and Residual Plots Most likely a linear regression will not fit the data perfectly. The residual (e) for each data point is the ________________________

Perfectly Linear Data

Draw a scatterplot from the given data.

Enter x-values into L1.Enter y-values into L2.

Use a calculator to find the linear regression for this data.

LinReg

y=ax+b

r2=

Linear regression equation:

Draw the linear regression on the same graph as the scatter plot (left).

Enter linear regression into Y1.

Use the table feature on the calculator to fill in the center column on the residual table (top right).

Complete the table.

Create a residual plot (right).

What do you notice about the residual plot?How does the linear

regression fit the data?

Page 3: Residuals and Residual Plots Most likely a linear regression will not fit the data perfectly. The residual (e) for each data point is the ________________________

Linear Data

A scatterplot and linearregression line are already drawn from the given data.

Enter x-values into L1.Enter y-values into L2.

How does the linear regression fit the data?

Use a calculator to find the linear regression for this data.

LinReg

y=ax+b

r2=

Linear regression equation:

Enter linear regression into Y1.

Use the table feature on the calculator to fill in the center column on the residual table (top right).

Complete the table.

Create a residual plot (right).

What do you notice about the residual plot?

Page 4: Residuals and Residual Plots Most likely a linear regression will not fit the data perfectly. The residual (e) for each data point is the ________________________

Non-Linear Data

A scatterplot and linearregression line are already drawn from the given data.

Enter x-values into L1.Enter y-values into L2.

How does the linear regression fit the data?

Use a calculator to find the linear regression for this data.

LinReg

y=ax+b

r2=

Linear regression equation:

Enter linear regression into Y1.

Use the table feature on the calculator to fill in the center column on the residual table (top right).

Complete the table.

Create a residual plot (right).

What do you notice about the residual plot?

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