Find the residual values, and use the graphing calculator tool to make a residual plot.

A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries negative 3.5, negative 2.9, negative 1.1, 2.2, 3.4. The third column is labeled predicted with entries negative 1.1, 2, 5.1, 8.2, 1.3. The fourth column is labeled residual value with all entries blank.
Does the residual plot show that the line of best fit is appropriate for the data?

Yes, the points have no pattern.
No, the points are evenly distributed about the x-axis.
No, the points are in a linear pattern.
Yes, the points are in a curved pattern.

Explanation:

1. Write the table with the data:

  x      given     predicted       residual

  1       - 3.5         - 1.1

  2      - 2.9           2

  3       - 1.1            5.1

  4        2.2           8.2

  5        3.4           1.3

2. Complete the column of residuals

The residual is the observed (given) value - the predicted value.

Thus, the complete table, with the residual values are:

  x      given     predicted       residual

  1       - 3.5         - 1.1                 - 2.4

  2      - 2.9           2                  - 4.9

  3       - 1.1            5.1                - 6.2

  4        2.2           8.2               - 6.0

  5        3.4           1.3                   2.1

3. Residual plot

You must plot the last column:

  x      residual

  1       - 2.4

  2      - 4.9

  3       - 6.2

  4       - 6.0

  5        2.1

See the plot attached.

Does the residual plot show that the line of best fit is appropriate for the data?

Ideally, a residual plot for a line of best fit that is appropiate for the data must not show any pattern; the points should be randomly distributed about the x-axis.

But the points of the plot are not randomly distributed about the x-axis:  there are 4 points below the x-axis and 1 point over the x-axis: there are more negative residuals than positive residuals.  This is a pattern. Also, you could say that they show a curve pattern, which drives to the same conclusion: the residual plot shows that the line of best fit is not appropiate for the data.

Thus, the conclusion should be: No, the points have a pattern.

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