Question

The initial visual impact of a scatter diagram depends on the scales used on the x and y axes. Consider the following data. x 1 2 3 4 5 6 y 1 4 6 3 6 7 (a) Make a scatter diagram using the same scale on both the x and y axes (i.e., make sure the unit lengths on the two axes are equal). Draw the straight line that best fits the data points. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (b) Make a scatter diagram using a scale on the y axis that is twice as long as that on the x axis. Draw the straight line that best fits the data points. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (c) Make a scatter diagram using a scale on the y axis that is half as long as that on the x axis. Draw the straight line that best fits the data points. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) How do the slopes (or directions) of the three lines appear to change? Stretching the scale on the y-axis makes the line appear steeper. Shrinking the scale on the y-axis makes the line appear flatter. The slopes do not change in actual value. Stretching the scale on the y-axis makes the line appear steeper. Shrinking the scale on the y-axis makes the line appear flatter. The slopes change in actual value. Stretching the scale on the y-axis makes the line appear flatter. Shrinking the scale on the y-axis makes the line appear steeper. The slopes do not change in actual value. Stretching the scale on the y-axis makes the line appear flatter. Shrinking the scale on the y-axis makes the line appear steeper. The slopes change in actual value.

Answer 1

Solution:

Given

X	1	2	3	4	5	6
Y	1	4	6	3	6	7

a) A  scatter diagram using the same scale on both the X and Y axes:   

b) A scatter diagram using a scale on the y axis that is twice as long as that on the X axis:

c) A scatter diagram using a scale on the y axis that is half as long as that on the X axis:

d) The slopes (or directions) of the three lines appear to change:

  Stretching the scale on the y-axis makes the line appear steeper. Shrinking the scale on the y-axis makes the line appear flatter. The slope do not change in actual value.

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