To Lecture Notes

LSP 121 -- 9/28/10

Review Questions

1. What does the correlation between two variables x and y tell you?

2. Which of these datasets has a linear relationship between them?

   x y 1 3 2 4 3 5 4 6 5 4 6 2 7 0

   x y 1 9 2 4 3 1 4 0 5 1 6 4 7 9

   x y 2.0 1.0 3.0 1.0 3.5 2.2 4.0 3.0 5.0 5.0 3.0 2.5 4.0 4.0

   x y 5.0 3.0 3.0 5.0 4.0 4.0 4.0 3.0 2.5 5.0 2.0 6.0 3.0 7.0

   Ans: (1) the relationship is a piecewise linear one, not linear, (2) the relationship is a perfect quadratic one, not linear, (3) the relationship is a positive linear one; the points form an ellipse-shaped cloud, (4) the relationship is a negative linear one; the points form an ellipse-shaped cloud.

3. What is the correlation of x with itself?

   Ans: 1, it is a perfect positive linear relationship.

4. Explain the difference between the independent and dependent variables in a bivariate dataset.

   Ans: The dependent variable depends on the independent variable, changes in the independent variable causes the dependent variable to change, on the average.

5. What does the R-squared value tell you about the relationship between the variables x and y?

   Ans: The R-squared value is the proportion of variation in the dependent variable that can be explained by the variation in the independent variable.

6. What should you check in the Variable View of the SPSS Dataset Editor after you create or load a new column of values?

   Ans: The variable name, variable type (numeric or string), number of digits after the decimal, the measure (Nominal, Ordinal, Scale).

More about Correlation

• Correlation does not necessarily imply causation.

• If X is correlated with Y, there could be some third variable that causes both.

• Example:   The price of rum in Havana is highly correlated with minister's salaries in New England. Is there causation?

• For a correlation between X and Y to imply causation,
  1. X must precede Y in time,

  2. the causation must be plausable,

  3. common causes from other variables must be ruled out.

• The correlation is misleading if there is a nonlinear relationship between the variables.
  Example 1:   There is a perfect polynomial relationship between X and Y, but the correlation is -0.368.

• Outliers can distort the correlation:
  Example 2:   Without the outlier, the correlation is 1; with the outlier the correlation is 0.514.

  Example 3:   Without the outlier, the correlation is 1; with the outlier the correlation is 0.522.

• Analyze the Hampster Dataset. Form the scatterplot and find the correlation and R-squared value.

Expanded Values for a Nominal Variable

• Suppose we have an SPSS dataset with a column named "gender". This column consists of values 1 and 2, where 1 represents Female and 2 represents Male.

• Change the the Variable View of the Dataset Editor:
  Change the Measure of gender to Nominal.

  Set the Label to "Gender of Respondent".

  Use the dropdown box of Values to set the expanded value descriptions of gender to 1 = "Female" and 2 = "Male".

• Now run Analyze >> Descriptive Statistics >> Frequencies for the gender column. Notice that the expanded values Female and Male are used in the output report.

Work on Activities

• Finish Activity 6 and Activity 5.