Group Project by mikesanye

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									                    Project #3 by Daiva Kuncaite
                        Problem 31 (p. 190)

Researchers wondered
whether the size of
person’s brain was related
to the individual’s mental
capacity. To find out the
answer first I will add
provided data in the book
to the spss system.
Data
Provided data in the book
table I added in the spss
sytem . I construct three
variables for gender, MRI
count and IQ score.
a) draw a scatter diagram,
treatning MRI count as
explanatory variable and IQ
as response.
STEP 1:
• I choose Graphs > Scatter
to open the Scatter plot
dialog box.
• select Simple in order to
create simple scatter plot.
•Then I click Define.
STEP 3
•I paste the variable MRI
count in the X axis ,
because it is explanatory
variable and IQ score I
paste in the Y axis box
because it is a response
variable.
• Then I click OK.
Result:
•The output window will
show the scatter plot .
• From the scatter diagram
I can see that there is
positive linear relationship
between MRI and IQ
score.
b) Compute the linear
correlation coefficient
between MRI count and IQ
score. Is the MRI count
and IQ score are linearly
related?
Step 1:


•I use the program Analyze
> Correlate > Bivariate in
order to get the linear
correlation coefficient.
Step 2

•   I place MRI count and IQ
    score in the variable window
•    Click OK
Step 3:

• The output window will show
  correlation table.
• The Person Correlation between
  the MRI count and IQ score is
  0.548, which indicates that there
  is a positive weak linear
  relationship between those two
  variables . Larger the MRI count,
  larger the IQ score.
C) Draw a scatter diagram by using
different plotting symbol for each gender.
Step 1:


• I use the program Graph >
  Scatter... It shows me a scatter
  plot box where I chose function
  Simple and click Define.
• It opens simple scatter plot box. I
  place MRI count in X – axis box
  (explanatory variable), IQ score in
  Y-axis box ( response variable)
  and gender in Set Markers by box
  in order to create different
  symbols for each gender.
• Click OK
Step 2:


• The output window show the
  scatter plot in which male
  represents green color and
  female represents red color.
• From the diagram we can see
  clearly that females tend to have
  lower MRI counts. After the
  separation we can see that weak
  linear relationship seems to
  disappear. Neither of group
  presents any clear relationship
  between IQ and MRI count
  d) Compute the linear correlation
  coefficient for females and males
  separately. Do you believe that MRI
  count and IQ score are linearly related?
  Step1:
• First, I select the cases for female
  only from the data by using Data >
  Select Cases
• It opens select cases window
  where I’m going to choose the
  command If condition is satisfied
• I click OK.
Step 2:


• Select cases: if window opens and
  in the variable bow I put
  gender=‘F’ in order to get
  selected all females from the data
  set.
• Click continue.
Step 3:


• Computer automatically selected
  all female participants in the
  date.
• Now I can find out the linear
  correlation coefficient between
  MRI count and IQ score for
  females only by using Analyze >
  Correlate > Bivariate
Step 4:


• In the Bivariate correlation
  window I put MRI count and IQ
  score in the variable box.
• Click OK.
Step 5:


• The output window will show
  that the linear correlation
  coefficient for females ( r) is
  0.359
Step 6:


• I repeat the steps from 1 to 2, just
  in the select case if: window I put
  gender=‘M’ in order to select all
  Male participants in the data set.
• Click Continue.
Step 7:


• The computer automatically
  selected Male only and now I can
  compute the linear correlation
  coefficient between MRI count
  and IQ score for males only by
  using Analyze > Correlate>
  Bivariate
• Click OK
Step 8:


• The output window will show the
  linear correlation coefficient ( r)
  for males only which is 0.236
Step 9:


• In conclusion it appears that
  there is no linear relationship
  between brain size (MRI count)
  and IQ score.
• The moral of the story is to be
  aware of the lurking variables.
                 Problem 23 (p.207)
• I use same data set for the
  problem 23.
a) Find the least- squared regression
        line.
        Step 1:
• In order to find the least –
  squared regression line I use the
  program Analyze > Regression>
  Linear
Step 2:


• It opens linear regression window
  where I place MRI count in the
  Independent variable box and IQ
  score in the Dependent variable
  box.
• Click OK
Step 3:


• The output window will show 4
  tables. I use the last table to
  determine the least - squares
  regression line.
• The Coefficient table shows that
  the values of Y – intercept
  (109.894) and slope
  (0.00002863).
• The regression equation is: Y (hat)
  = 0.00002863 +109.8940
b) What do you notice about the value of the slope? Why does this result
seems reasonable based on the scatter diagram and linear correlation
coefficient obtained in Problem 31 (p. 190)

• The slope is closed to 0, which is due to the weak linear relationship that is
  presented. Also the size of the values for MRI count is very large (hundreds
  of thousands).
• This result seems reasonable in comparison with the scatter diagram and
  linear correlation coefficient obtained in the problem 31 (p.190)
c) When there is no relation between the explanatory and response variable we use
the mean value of the response variable, y (bar), to predict. Predict the IQ of an
individual whose MRI count is 1,000,000. Predict the IQ of an individual whose MRI
count is 830,000

•   There is no apparent relation
    between MRI and IQ.
•   In both cases we use y( bar) as our
    estimate.
•   I find the mean of IQ score by using
    program Analyze > Descriptive
    Statistic> Frequency
Step 2:


• In the Frequency variable window
  I add MRI count and IQ score.
• I click on Statistics bar.
• It opens statistics window in
  which I mark mean in order to get
  the mean of the IQ score.
• Click Continue in the Statistics
  window and then OK in the
  Frequency window.
Step 3:


• The mean for IQ score is equal to
  136.40
• Since in both cases we use y bar
  as our estimate, then y hat = y
  bar = 136.40
               Consumer reports: Fit to drink

• Concern about water quality and
  taste have made home filtering
  increasingly popular.
• To test chloroform and lead
  removal was added concentrated
  amounts of both to the water.
• Every few days the water was
  analyzed and measured
  chloroform and lead content.
• I added the data in the spss
  system which contains only lead
  measurments.
a) Construct a scatter diagram of the
       data by using % Lead
       Removed as the response
       variable.
• I use the program Graph> Scatter
• It opens scatter plot window
  where I chose Simple in order to
  construct a simple scatter
  diagram.
• Click Define.
• It opens Simple Scatter Plot
  window where I put % Lead
  Removed to the Y axis as
  response variable and Gallons
  Processed to the X axis as
  explanatory variable.
• Click OK
b) Does the relationship between
NO. Gallons Processed and % Lead
Removed appear to be linear?

• The output window shows the
  scatter diagram.
• The relationship between No.
  Gallons Processed and % Lead
  removed appear to be positive
  linear.
 c) Calculate the linear correlation
 coefficient . Based on the scatter diagram
 in part a) and the answer in part b), is this
 measure useful? What is R squared?
 Interpret R squared.
 Step 1:
• I calculate the linear correlation
  coefficient by using program
  Analyze > Correlate > Bivariate
• It opens Bivariate window.
• I place No. Gallons Processed and
  % Lead Removed to the variable
  window.
• Click OK.
Step 2:


• The output will show the
  correlation table.
• The linear correlation coefficient r
  = 0.868, which means that there
  is a positive linear relationship
  between two variables.
Step 3:


• I compute the least –squares
  regression line by using program
  Analyze> Regression > Linear
• I t opens linear regression
  window in which I place % Lead
  removed in Dependent variable
  box and No. Gallons Processes in
  the Independent variable box .
• Click OK.
Step 4:


• The output window will show 4
  tables.
• In the Model Summary table we
  find R squared.
• R squared = 0.753
• It means that 75.3 % of the
  variation in the values % Lead
  Removed explained by the linear
  relation between two variables.
d) Fit the linear regression model to
these data.
Step 1:

• In the output window I double
  click the scatter diagram.
• The computer will give me SPSS
  Chart Editor Window.
• I use program Chart > Options>
  which gives me scatter plot
  options window.
• I mark box Total .
• I click on the bar Fit Options..
Step 2:


• After clicking Fit Options new
  window opens in which I mark
  Linear Regression Icon.
• Click Continue.
• Click OK.
Step 3:


• The scatter diagram
  with a linear regression
  model

								
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