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Thorne and Giesen Book Cover
Statistics for the Behavioral Sciences, 4/e
Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State
Correlation and Regression

Problems

  1. On the basis of your experience, decide whether the following pairs of variables are positively, negatively, or not correlated.

    1. amount of alcohol consumed and speed of reaction to a suddenly appearing stimulus.

    2. ratings of physical attractiveness of husband–wife pairs

    3. IQ scores and the number of trials to learn a list of nonsense syllables for students in a general psychology class

    4. sales of McDonald’s hamburgers per day in a city and the number of people committed per day to a state mental institution

    5. amount of time spent in practice and the average golf score

    6. number of siblings and the likelihood of developing lung cancer

    7. length of depression and the probability of suicide

  2. The scores of 10 people on standardized scales of introversion and shyness are shown here (high scores on each scale indicate high introversion and shyness).

    Person Introversion Shyness
    1 17 22
    2 6 4
    3 12 10
    4 13 8
    5 19 11
    6 20 18
    7 9 10
    8 4 3
    9 8 10
    10 21 16

    Make a scatterplot of the data. Which class of correlation is revealed in the graph?

    Compute r, and test it for significance. How much of the variability is accounted for by r?

  3. Using the information in Problem 2, compute the regression equation for Y. Use the equation to predict the shyness score of a person with an introversion score of 15.

  4. In a physiological psychology class, the first and last exam scores were as follows:

    Student First Score Last Score
    A 60 75
    B 88 84
    C 99 98
    D 62 73
    E 86 91
    F 92 91
    G 99 97
    H 78 90
    I 92 93
    J 62 78
    K 61 64
    L 75 82
    M 92 92
    N 86 76
    O 58 79
    P 32 46
    Q 54 67

    Compute r, and test it for significance.

    Find the regression equation for Y. Use the equation to predict a last exam score for a student who made a 95 on the first test. Do the same for a student who made a 55 on the first test.

  5. Ten female monkeys with male offspring are assigned ratings on a dominance test. The ratings of their male offspring are also determined. Assume the ratings are ordinal level measurement at best. Is there a relationship between the ratings? Test your correlation coefficient for significance.

    Female Number Dominance Ratings Ratings of Offspring
    1 10 8
    2 9 10
    3 9 8
    4 7 6
    5 6 6
    6 5 6
    7 5 4
    8 5 5
    9 3 4
    10 2 1

  6. A group of students was asked to estimate the amount of time each spends per day reading the newspaper. Then each student was given a 20-item recognition test of current events. The paired scores are:

    Student Time in Minutes Score
    A 25 12
    B 40 13
    C 55 18
    D 10 8
    E 5 5
    F 5 3
    G 30 10
    H 45 15

    What is the degree of relationship between the variables? Is it significant? How much of the variability in the data is accounted for by r?

  7. Using figures from Consumer Reports, a consumer wants to see whether there is any relationship between the weight of a car and the gas mileage it gets in city driving. The following pairs of scores are taken from the annual car buying guide:

    Car Weight in Thousands of Pounds mpg in Town
    1 2.6 17.4
    2 2.1 20.8
    3 2.2 19.2
    4 2.0 19.8
    5 3.2 13.9
    6 2.7 13.4
    7 3.4 11.8
    8 3.8 10.3
    9 3.9 9.5

    Compute the correlation coefficient, and test it for significance.

  8. Using the data from Problem 7, find the regression equation for Y. What gas mileage can the consumer expect from a car weighing 4,300 pounds?

  9. In a study of the parents of schizophrenic children, letters have been independently rated by two psychiatrists for the presence of contradictory ideas and feelings. The rating scale assigns numbers from 0 to 7, with higher numbers indicating more contradictions. Assume the ratings are ordinal scale measurement at best. Compute a correlation coefficient, and test it for significance.

    Letter Rater A Rater B
    A 3 7
    B 2 4
    C 5 3
    D 7 6
    E 0 5
    F 1 4
    G 2 4
    H 4 2

  10. Two experimenters have independently rated the handling characteristics of 12 rats. Compare the correlation between the ratings of Experimenters A and B, assuming that the ratings are ordinal scale measurement at best. Test your coefficient for significance.

    Rat Experimenter A Experimenter B
    1 15 13
    2 13 14
    3 10 11
    4 5 5
    5 8 10
    6 6 8
    7 3 4
    8 7 6
    9 7 5
    10 2 1
    11 2 2
    12 2 3

  11. The following pairs of scores are heart rate values measured by a physiograph for subjects looking at different stimuli. Compute the most appropriate correlation coefficient, and test it for significance.

    Subject Stimulus A Stimulus B
    1 65.3 71.8
    2 75.7 73.5
    3 85.6 99.3
    4 73.7 81.7
    5 69.5 75.7
    6 68.2 73.5
    7 70.1 79.8
    8 72.5 70.3
    9 71.0 85.3
    10 83.5 107.1

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