Question

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

Answer 1

Answer:

(3,0)

Explanation:

Answer 2

Answer:

• No, the points are evenly distributed about the x-axis.

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.

• residual = given - predicted.

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.

• 1. "Yes, the points have no pattern": false, because as shown, the points do have a pattern, which makes the residual plots does not show that the line of best fit is appropiate for the data.

• 2. "No, the points are evenly distributed about the x-axis": true. As already said the points have a pattern. It is a curved pattern, and this shows the line of best fit is not appropiate for the data.

• 3. "No, the points are in a linear pattern": false. The points are not in a linear pattern.

• 4. "Yes, the points are in a curved pattern": false. Because the points are in a curved pattern, the residual plot shows that the line of best fit is not appropiate for the data.