Given are five observations for two variables,xandy.

x_i 1 2 3 4 5

y_i 4 7 6 10 13

(a)

Develop a scatter diagram for these data.

A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis.

A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 13 on the vertical axis.

A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 12 on the vertical axis.

A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis.

(b)

What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

• There appears to be no noticeable relationship betweenxandy.
• There appears to be a positive linear relationship betweenxandy.
• There appears to be a negative linear relationship betweenxandy.

(c)

Try to approximate the relationship betweenxandyby drawing a straight line through the data.

A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. A straight line with positive slope is imposed onto the diagram to approximate the relationship betweenxandyimplied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 13 on the vertical axis.

A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. A straight line with negative slope is imposed onto the diagram to approximate the relationship betweenxandyimplied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis.

A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. A straight line with negative slope is imposed onto the diagram to approximate the relationship betweenxandyimplied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis.

A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled:x. The vertical axis ranges from 0 to 18 and is labeled:y. A straight line with positive slope is imposed onto the diagram to approximate the relationship betweenxandyimplied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 12 on the vertical axis.

(d)

Develop the estimated regression equation by computing the values ofb₀

andb₁

usingb₁=(x_ix)(y_iy)

(x_ix)²

andb₀=yb₁x.

=

(e)

Use the estimated regression equation to predict the value ofywhenx=2.