Question 1147075: Given are five observations for two variables, x and y.
xi
1 2 3 4 5
yi
2 8 6 11 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 starting in the upper left corner of the diagram. The first 2 points are between 11 to 13 on the vertical axis. The next 3 points are between 2 to 8 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 2 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 a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 2 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 1 to 12 on the vertical axis.
Correct: Your answer is correct.
(b)
What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
There appears to be a negative linear relationship between x and y.
There appears to be a positive linear relationship between x and y.
There appears to be no noticeable relationship between x and y.
Correct: Your answer is correct.
(c)
Try to approximate the relationship between x and y by 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 negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 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 11 to 13 on the vertical axis. The next 3 points are between 2 to 8 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 between x and y implied 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 2 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 positive slope is imposed onto the diagram to approximate the relationship between x and y implied 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 1 to 12 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 between x and y implied 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 2 to 13 on the vertical axis.
Correct: Your answer is correct.
(d)
Develop the estimated regression equation by computing the values of
b0
and
b1
using
b1 =
Σ(xi − x)(yi − y)
Σ(xi − x)2
and
b0 = y − b1x.
ŷ =
Incorrect: Your answer is incorrect.
(e)
Use the estimated regression equation to predict the value of y when
x = 2.
Answer by ikleyn(52903)   (Show Source):
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