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Correlation and Regression Computations

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Correlation and Regression

Lisa F. Peters
University of Phoenix

Correlation and Regression

13.12 Exercises 1 thru 24
2. For each of the following situations, create a scatterplot of the data and describe the nature, direction, and strength of the relationship.
a. A set of parents hypothesize there is a negative relationship between the average number of hours their children spend on the Internet and their scores on a recent school quiz (range = 0-100).

b. A college counselor hypothesizes that the farther students live from campus (in miles), the less they feel they are part of the school community (1 = low, 10 = high).

c. A publishing company develops a new college admissions test and hypothesizes that scores on the test are positively related to academic achievement in college. The company administers the test to a sample of college students (possible scores range from 0-100) and collects college grade point averages (GPAs) of the students.

4. For each of the following, calculate the degrees of freedom (df) and identify the critical value of r.
a. N = 21, a = .05 (two-tailed)
b. N = 40, a = .05 (two-tailed)
c. N = 12, a = .05 (one-tailed)
d. N = 120, a = .05 (one-tailed)
12. Earlier in this chapter, we discussed a study that examined the relationship between the amount of time students take to complete a test and their scores on the test (Herman, 1997). The two variables in this study were Time (the number of minutes taken by each student to finish the examination) and Exam score (the number of correct answers for each student, ranging from 0 to 100). The researcher in this study wished to test the hypothesis that the more time students take to finish an exam, the lower their score on the exam. In other words, there is a negative relationship between Time and Exam score. The data for the 32 students in this study are listed on page 636 (note that the scatterplot and descriptive statistics for these data were provided earlier in this chapter).

a. State the null and alternative hypotheses (H0 and H1) (use a non-directional H1).
b. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom (df).
(2) Set alpha (α), identify the critical values, and state a decision rule.
(3) Calculate a statistic: Pearson correlation (r).
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.
(6) Calculate a measure of effect size (r2).
c. Draw a conclusion from the analysis.
d. Relate the result of the analysis to the research hypothesis.
16. Calculate the linear regression equation for each of the situations presented earlier in Exercise 1 and draw the regression equation into its scatterplot.

Examining a figure such as a scatterplot provides an initial indication of how scores on two variables are associated with each other. Looking at the scatterplot in Figure 13.1, we observe that there is a general tendency for the ratings of a face to be similar for the 39 ms and 1700 ms conditions. For example, a low (or high) threatening rating for a face in the 39 ms condition is associated with a low (or high) threatening rating for the same face in the 1700 ms condition. The next section discusses how the relationship between two variables may be described and characterized.

20. Calculate the Spearman rank-order correlation (rs) for each of the following pairs of ranks.
a.
b.

c.

References
Tokunaga, H. T. (2016). Measures of central tendency. Fundamental Statistics for the Social and
Behavioral Sciences. SAGE Publications, Chptr 13.

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Solution Summary

The solutions are provided in the Word file. The computations were performed using the Excel file provided.

Solution Preview

The solutions are provided in the Word file. The computations were performed using the Excel file provided.

13.12

2) The Excel file shows how the scatter plots were created.
a)

Nature: approximately linear, the more hours one spends on the internet, the lower the quiz score.
Direction: negative
Strength: medium since r = 0.69

b)

Nature: no apparent relationship
Direction: none
Strength: weak since r = 0

c)

Nature: approximately linear, the higher the test score, the higher the college GPA
Direction: positive
Strength: medium since r = 0.66

4)
Refer to a table for Critical Values of the Pearson Correlation to find the critical r values below. I used the following table:
http://faculty.fortlewis.edu/chew_b/Documents/Table%20of%20critical%20values%20for%20Pearson%20correlation.htm

a)
df = 21 - 2 = 19
critical r = ...

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  • BSc, California State Polytechnic University, Pomona
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