Correlations Exercises
Question 1
The correlation matrix shows the strength and the direction of the correlation between two variables. Correlation ranges between -1 and 1, with values closer to -1 showing a strong negative correlation while values closer to 1 show a stronger positive correlation. The strongest correlation in the analysis will be closest to one of the correlation value limits (Gray & Grove, 2020). Thus, the strongest correlation in the matrix is -0.316 between the number of doctor visits in the last 12 months and the SF12: Physical health component score variables. The correlation of the two variables is also significant at a 1% level of significance. It implies that more hospital visits in the previous 12 months were associated with low physical health component scores. A strong correlation may indicate that one variable largely affects the outcome of the other variable in a particular direction.
Question 2
The weakest correlation in the correlation matrix is between Body Mass Index and SF12: Mental health component score, with a correlation value of -0.078. The weakest correlation approaches value zero since it shows that the variables have neither a strong positive nor a strong negative correlation. The correlation implies that, to a small extent, a high Body Mass Index is negatively associated with lower mental health component scores. A weak correlation indicates that the explanatory variable does not explain the change in the outcome variable to a large extent (Newman, 2016). However, the weakest correlation value between the two variables is significant at a 5% level of significance.
Question 3
The number of correlations in a correlation matrix indicates the relationship between the variables under study and how they relate to each other. The various combinations between the different variables give the number of original correlations in a matrix. In the analysis output, there are six correlations.
Question 4
The diagonal of the matrix shows the correlation between the same variable that appears on the row side and column. Usually, a correlation between a variable and itself will be 1. This is because the values being correlated are the same for the same participant. For instance, the body mass index will be the same for the row and column values. The sample sizes at the diagonal of the matrix further confirm that the same variables are being correlated.
Question 5
The correlation value between the Body Mass Index variable and the Physical health component score is -0.134. This indicates that the two variables are weakly negatively correlated. It indicates that a high body mass index is associated with low physical health component scores, which implies that a high BMI is associated with low physical health scores.
Question 6
The variable that is strongly correlated with BMI is the physical health component score. The two variables have a correlation coefficient of -0.134, which is significant at a 1% level of significance. The sample size used to determine the association between these two variables is 866 participants. Since the physical health component variable has the strongest correlation with the BMI, it shows that the variables predict each other better compared to any other variable combinations.
Question 7
The mean for the number of doctor visits in the previous month is 6.80, with a standard deviation of 12.720 for a sample of 997 participants. This indicates that 68% of visits within the first standard deviation deviate from the mean within the range of 0 to 12.720 points, as Field (2018) suggests. The mean body mass index is 29.222, with a standard deviation of 7.38 for a sample of 970 participants. This also indicates that the first standard deviation will contain 68% of the data.
Question 8
For the second data set used to produce the scatter plot, the variables considered are BMI and weight in pounds. The mean weight for the participants was 171.46 pounds, with a standard deviation of 45.44 for a sample of 971 participants. The same sample of 970 participants was used to determine BMI statistics, and the mean BMI was 29.22, with a standard deviation of 7.38.
Question 9
The second correlation matrix shows the correlation between body mass index and weight in pounds. The correlation value between the two variables is 0.937, which is significant at a 1% level of significance. The correlation value indicates that the two variables have a strong positive correlation, which indicates that the variables predict each other to a large extent. Particularly, the strong positive correlation between the variables indicates that a high value of weight in pounds will be associated with a high body mass index for the participants.
Question 10
The scatter plot shows the relationship between two continuous variables to visually understand how the two variables relate. The independent variable in the data set is BMI, while the dependent variable is weight in pounds. The distribution of the data points in the scatter plot and the gradient of the distribution indicate that the two variables are positively correlated (Rosnow & Rosenthal, 2013). That is, an increase in body mass index leads to an increase in weight in pounds. Data visualization enables the researcher to explain the findings easily to a general audience without background knowledge of statistics.
References
Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. New York; Cengage Publishers.
Gray, J. R., & Grove, S. K. (2020). Burns and Grove’s the practice of nursing research: Appraisal, synthesis, and generation of evidence (9th Ed.). Elsevier.
Newman, M. (2016). Research methods in psychology (2nd Ed.). San Diego, CA: Bridgepoint Education, Inc.
Rosnow, R. L., & Rosenthal, R. (2013). Beginning Behavioral Research: A Conceptual Primer (Seventh Edition). Pearson Education Inc. New York.
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Question 
THE ASSIGNMENT: (2–3 PAGES)
Answer the following questions using the Week 6 Correlations Exercises SPSS Output provided in this week’s Learning Resources.
Correlations Exercises
What is the strongest correlation in the matrix? (Provide the correlation value and the names of variables)
What is the weakest correlation in the matrix? (Provide the correlation value and the names of variables)
How many original correlations are present on the matrix?
What does the entry of 1.00 indicate on the diagonal of the matrix?
Indicate the strength and direction of the relationship between body mass index (BMI) and physical health component subscale.
Which variable is most strongly correlated with BMI? What is the correlational coefficient? What is the sample size for this relationship?
What is the mean and standard deviation for BMI and doctor visits?
What is the mean and standard deviation for weight and BMI?
Describe the strength and direction of the relationship between weight and BMI.
Describe the scatterplot. What information does it provide to a researcher?