Project #3 by Daiva KuncaiteProblem 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.

DataProvided 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