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Homework - Correlation

DIRECTIONS: Be sure to show all work neatly. Attach Minitab output when required and do mark it up and/or label it to clearly indicate that you understand what is relevant in the output. More specifically, describe what you see in the scatter plots (and make sure they are labeled clearly enough to be readable) and whether the correlations you calculate agree with what you obtained when calculating by hand.

Problems

  1. There are three observers (1, 2, & 3) simultaneously scoring the aggressive behavior (defined as hitting) for 5 different children (labeled A through E) in a playground. The observers scores are as follows. Compute the interobserver reliabilities (i.e., correlations between observers) as well as the means for each observer. Do this by hand as well as using MTB. Draw some conclusions from your analysis (e.g., what does the analysis tell you about the data?). (45 points)

    Child Observer
    1
    2
    3
    A
    4
    8
    5
    B
    2
    3
    1
    C
    5
    8
    4
    D
    3
    5
    2
    E
    8
    10
    7

  2. Professor Prit E. Nosy is interested in the relationship between nose length and good looks in college men. So he finds five men who have noses, measures their noses, and ranks them according to their good looks (1=most good looking). Using the data below and the appropriate correlational coefficient, illustrate the correlation and determine the correlation coefficient between nose length and good looks. Finally, describe the correlation and discuss what it means? (Note that when doing the ranking, do it by hand as well as with Minitab.) (45 points)

    Person
    Nose length
    (mm)
    Looks
    A
    42
    2
    B
    40
    4
    C
    51
    5
    D
    37
    3
    E
    38
    1

Multiple Choice (10 points)

  1. If the correlation between two variables is -1.00, it would indicate that
    a. there is no relationship between the two variables.
    b. while there is some relationship between the two variables, it is of the lowest possible degree.
    c. you cannot predict the value of one variable if you knew the value of the other.
    d. the two variables are perfectly related.

  2. When using Pearson's r,
    a. the data must be ordinal.
    b. we wish to find a causal relationship.
    c. r=.44 has greater predictive value that r=-.44.
    d. the two variables must be related in a linear fashion.

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