Question

The following data were used in a regression study.

Observation	1	2	3	4	5	6	7	8	9
xi	2	3	4	5	7	7	7	8	9
yi	3	5	4	7	4	6	9	4	11

(a)

Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.)

ŷ =

(b)

Construct a plot of the residuals.

A residual plot has 9 points plotted on it. The horizontal axis ranges from 0 to 10 and is labeled: x. The vertical axis ranges from −4 to 4 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. 4 points lie below the line and 5 lie above it. The points tend to become farther away from the line as x increases. The approximate locations of the points are:

• (2, 0.4),
• • (3, −0.9),
  • • (4, 0.7),
    • • (5, −1.6),
      • (7, 2.7),
      • • (7, 0.7),
        • • (7, −2.3),
          • • (8, 3.3),
            • • (9, −3.0).

A residual plot has 9 points plotted on it. The horizontal axis ranges from 0 to 10 and is labeled: x. The vertical axis ranges from −4 to 4 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. 5 points lie below the line and 4 lie above it. The points tend to become closer to the line as x increases. The approximate locations of the points are:

• (2, 3.0),
• • (3, −3.3),
  • • (4, 2.3),
    • • (5, −0.7),
      • (7, −2.7),
      • • (7, 1.6),
        • • (7, −0.7),
          • • (8, 0.9),
            • • (9, −0.4).

A residual plot has 9 points plotted on it. The horizontal axis ranges from 0 to 10 and is labeled: x. The vertical axis ranges from −4 to 4 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. 4 points lie below the line and 5 lie above it. The points tend to become closer to the line as x increases. The approximate locations of the points are:

• (2, −3.0),
• • (3, 3.3),
  • • (4, −2.3),
    • • (5, 0.7),
      • (7, 2.7),
      • • (7, −1.6),
        • • (7, 0.7),
          • • (8, −0.9),
            • • (9, 0.4).

A residual plot has 9 points plotted on it. The horizontal axis ranges from 0 to 10 and is labeled: x. The vertical axis ranges from −4 to 4 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. 5 points lie below the line and 4 lie above it. The points tend to become farther away from the line as x increases. The approximate locations of the points are:

• (2, −0.4),
• • (3, 0.9),
  • • (4, −0.7),
    • • (5, 1.6),
      • (7, −2.7),
      • • (7, −0.7),
        • • (7, 2.3),
          • • (8, −3.3),
            • • (9, 3.0).

Do the assumptions about the error term seem to be satisfied?

The plot suggests curvature in the residuals indicating that the error term assumptions are satisfied.The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are not satisfied.    The plot suggests a funnel pattern in the residuals indicating that the error term assumptions are not satisfied.The plot suggests a funnel pattern in the residuals indicating that the error term assumptions are satisfied.The plot suggests curvature in the residuals indicating that the error term assumptions are not satisfied.

Answer 1

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