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Solved: Does Size Matter?(Refer to Size Matter?Researchers
Chapter 3, Problem 26AYU(choose chapter or problem)
Does Size Matter? (Refer to Problem Does Size Matter?) Researchers wondered whether the size of a person’s brain was related to the individual’s mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. MRI scans were performed at the same facility for the subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with a nonzero gray scale in each of the 18 images, and the total count served as an index for brain size.
(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Comment on what you see.
(b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly related?
(c) A lurking variable in the analysis is gender. Draw a scatter diagram treating MRI count as the explanatory variable and
IO as the response variable, but use a different plotting symbol for each gender. For example, use a circle for males and a triangle for females. What do you notice?
(d) Compute the linear correlation coefficient between MRI count and IQ for females. Compute the linear correlation coefficient between MRI count and IO for males. Are MRI count and IQ linearly related? What is the moral?
Questions & Answers
QUESTION:
Does Size Matter? (Refer to Problem Does Size Matter?) Researchers wondered whether the size of a person’s brain was related to the individual’s mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. MRI scans were performed at the same facility for the subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with a nonzero gray scale in each of the 18 images, and the total count served as an index for brain size.
(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Comment on what you see.
(b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly related?
(c) A lurking variable in the analysis is gender. Draw a scatter diagram treating MRI count as the explanatory variable and
IO as the response variable, but use a different plotting symbol for each gender. For example, use a circle for males and a triangle for females. What do you notice?
(d) Compute the linear correlation coefficient between MRI count and IQ for females. Compute the linear correlation coefficient between MRI count and IO for males. Are MRI count and IQ linearly related? What is the moral?
ANSWER:
Answer :
Step 1
a) A scatter diagram treating MRI count as the explanatory variable and IQ as the response variable.
The scatter plot is given below.
b)
The formula of the linear correlation coefficient is
r =
Here we have to find the linear correlation coefficient between MRI count and IQ.
We are using excel to find the linear correlation coefficient between MRI count and IQ.
We have to follow the step by step.
We have to enter the data in excel.
Then the first column x values (MRI count ) and second column value y (IQ).
The formula of the linear correlation coefficient in excel is
=correl(x values select , y values select)
Then enter.
We get the linear correlation coefficient between MRI count and IQ.
The linear correlation coefficient between MRI count and IQ is 0.4940