Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant, that is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it i violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity. The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities x (in decibels), the experimental Weber fraction y (ir decibels) is shown. For these data, the least-squares regression line is î=3.1193 – 0.0941x. This line is shown in the scatter plot in Figure 1. Stimulus Intensity, x (in decibels) Weber fraction, Y (in decibels) 35 0.48 40 0.24 45 1.39 50 1.05 55 2.12 60 2.81 65 3.34 70 2.99 75 4.21 80 4.29 Figure 1 Send data to Excel Answer the following: 1. Fill in the blank: For these data, Weber fractions that are less than the mean of the Weber fractions tend to be paired with stimulus intensities that are Choose one the mean of the stimulus intensities. 2. According to the regression equation, for an increase of one decibel in stimulus intensity, there is a corresponding decrease of how many U decibels in the Weber fraction? 3. From the regression equation, what is the predicted Weber fraction (in decibels) when the stimulus intensity is 65 decibels? (Round your U answer to at least two decimal places.) 4. What was the observed Weber fraction (in decibels) when the stimulus intensity was 65 decibels?
Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant, that is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it i violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity. The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities x (in decibels), the experimental Weber fraction y (ir decibels) is shown. For these data, the least-squares regression line is î=3.1193 – 0.0941x. This line is shown in the scatter plot in Figure 1. Stimulus Intensity, x (in decibels) Weber fraction, Y (in decibels) 35 0.48 40 0.24 45 1.39 50 1.05 55 2.12 60 2.81 65 3.34 70 2.99 75 4.21 80 4.29 Figure 1 Send data to Excel Answer the following: 1. Fill in the blank: For these data, Weber fractions that are less than the mean of the Weber fractions tend to be paired with stimulus intensities that are Choose one the mean of the stimulus intensities. 2. According to the regression equation, for an increase of one decibel in stimulus intensity, there is a corresponding decrease of how many U decibels in the Weber fraction? 3. From the regression equation, what is the predicted Weber fraction (in decibels) when the stimulus intensity is 65 decibels? (Round your U answer to at least two decimal places.) 4. What was the observed Weber fraction (in decibels) when the stimulus intensity was 65 decibels?
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O REGRESSION AND CORRELATION
Predictions from the least-squares regression line
Weber's law, a concept taught in most Introduction to Psychology
courses, states that the ratio of the intensity of a stimulus to the "just
noticeable" increment in intensity is constant, that is, the ratio doesn't
depend on the intensity of the stimulus. The ratio is called the "Weber
圖
fraction," so a concise statement of Weber's law is that "the Weber
fraction is constant, regardless of the stimulus intensity." It turns out
that Weber's law is not so much a law as it is a rule of thumb, since it is
violated in many situations. For instance, for some auditory stimuli, the
Weber fraction does depend systematically on the stimulus intensity.
The following bivariate data are the experimental data obtained for one
listener in an auditory intensity discrimination task. For each of the ten
stimulus intensities x (in decibels), the experimental Weber fraction y (in
decibels) is shown. For these data, the least-squares regression line is
y = 3.1193 – 0.0941.x. This line is shown in the scatter plot in Figure 1.
Stimulus
Weber fraction, v
intensity, x
(in decibels)
(in decibels)
35
-0.48
40
-0.24
45
-1.39
50
-1.05
55
-2.12
60
-2.81
65
-3.34
70
-2.99
75
-4.21
80
-4.29
Figure 1
Send data to Excel
Answer the following:
1. Fill in the blank: For these data, Weber fractions that are less than
the mean of the Weber fractions tend to be paired with stimulus
the mean of the stimulus intensities.
Choose one
intensities that are
2. According to the regression equation, for an increase of one decibel
in stimulus intensity, there is a corresponding decrease of how many L
decibels in the Weber fraction?
3. From the regression equation, what is the predicted Weber fraction
(in decibels) when the stimulus intensity is 65 decibels? (Round your LU
answer to at least two decimal places.)
4. What was the observed Weber fraction (in decibels) when the
stimulus intensity was 65 decibels?
?
Explanation
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