Given are five observations for two variables,xandy.

xi	1	2	3	4	5
yi	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 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.

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.

(b)What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?There appears to be a positive linear relationship betweenxandy.There appears to be a negative linear relationship betweenxandy. There appears to be no noticeable 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 of

b₀

and

b₁

using

b₁=

(x_ix)(y_iy)

(x_ix)²

and

b₀=yb₁x.

=

(e)Use the estimated regression equation to predict the value ofywhen

x=4.