 2.03 Residuals

Worksheet
Residuals
1

The following tables show sets of data \left(x, y\right) and the predicted \hat{y} values based on a least squares regression line. Complete the tables by finding the residuals:

a
b
2

Complete the following tables of residuals:

a
b
3

If a residual is a positive value, is the actual value of the response variable above or below the least squares regression line?

4

If a measured point in a data set is below the least squares regression line, will the corresponding residual be positive or negative?

Residual plots
5

Construct the residual scatter plot of the following data sets:

a
b
6

The residual plot for a set of data is shown. Draw the scatter plot showing the original data.

7

The residual plot can help us decide if a linear model should be used for a raw set of data.

a

Explain when a linear model would be a good fit for a set of raw data.

b

Explain when a linear model would not be a good fit for a set of raw data.

8

For each of the following data sets:

i
Complete the table of residuals.
ii

Plot the residuals on a scatter plot.

iii

Determine if the model is a good fit for the data.

a

The table shows a company's costs, C (in millions), in week W.

The equation C = 3 W + 4 is being used to model the data.

b

The table shows a company's revenue, R (in millions), in week W.

The equation R = 3 W + 5 is being used to model the data.

9

The table below shows the residual values after a least-squares regression line has been fitted to a set of data:

a

Plot the residuals on a scatter plot.

b

Determine if a linear model is a good fit for the data.

10

For each of the data sets below:

i

Complete the table by finding the residuals.

ii

Plot the residuals on a scatter plot.

iii

Determine whether the original data has a linear or nonlinear relationship.

iv

Create a scatter plot for the original data.

a
b