# Correlation and Regression

Paper Outline

Correlation: The relationship between assertiveness and the tendency to express anger openly
Mean and standard deviation
Pearson r
P-Value
Effect of sample size on r and p values
Regression: Relationship between assertiveness and whether one holds anger “in”

R and its meaning
R2 and its meaning
F and its meaning
Standard coefficient
Confidence interval
Summary

Correlations
Relationship between assertiveness and the tendency to express anger openly

What are the means and standard deviations of the two variables, “rath” and “axout”?

For a total of 65 subjects, the mean for “rath” is 3.3902 with a standard deviation of .4330. On the other hand, 63 subjects had a mean of 2.1071 for “axout” with a standard deviation of .4276 (Table 1).

What is the Pearson r?

The Pearson correlation r between “rath” and “axout” is r = .286.

What is the p value (“significance level”)? What does this p value mean?

The 2-tailed significance value for this Pearson r is .023, which is less than .05, indicating that there is a significant relationship between “rath” and “axout”. It is therefore evident that there is a statistically significant relationship between assertiveness and the tendency to express anger openly (Table 2).

How does the n (sample size) of this sample affect the r and p values?

Field (2009) explains that the larger the sample size, the more true the reflection of the strength of the relationship between two variables. As such, a larger sample size, n, is likely to increase the value of r perhaps to a figure that is greater than .5 thus indicating a strong relationship between “rath” and “axout”. At the same time, the p value is deemed to reduce further below the significance level of .05, thus indicating a more statistically significant relationship. Reducing the sample size on the other hand reduces r and is likely to increase p values thus giving a false reflection of the relationship between the two variables.
Regression
Relationship between assertiveness and whether one holds anger “in”

R and its meaning

According to Table 4, there is a negative correlation between crowne-marlowe and axin, r = -.246. R is the correlation coefficient between the variables, in this case the correlation between assertiveness and holding anger “in.” The R value for this model is .246 indicating that there is a negative but weak relationship between tendency to hold anger “in” and assertiveness. In other words, the correlation between assertiveness and holding anger “in” is .246 (Table 5).

R2 and its meaning

The R squared value for this model is .061 which indicates that 6.1 percent of holding anger “in” is contributed by the individual’s assertiveness (Table 5). This is because the R squared value is used to determine the proportion of variance explained by the model (predictor).

F and its meaning

The F-test value for this model is 4.073 and the F-test determines the statistical significance of the model whereby if the F-test is significant, then the model is termed as fit. In this model, the F value is significant p = .048 (Table 6) indicating that an individual’s assertiveness is a significant variable in predicting the individual’s tendency to hold anger “in.”
The F ratio (4.073) means that fitting in the model (i.e. considering assertiveness) leads to a 4.073 increase in tendency to hold anger “in.” The p value associated with the F value is .048 i.e. F (1, 63) = 4.073, p = .048). The p value (significance value) indicates that the F value is statistically significant. In other words, there is a statistically significant change in holding anger “in” as a result of an individual’s assertiveness.

Standard coefficient

The standard coefficient for the variable axin is -.246. The standard coefficient for the variable axin is significant because the value is below .05, i.e. p = .048 (Table 7).
Significance means that the variables obtained from the computations can be relied upon to explain the relationship between the variables being examined. In other words, one unit change in axin causes a -.246 change on crowne-marlowe.
The standardized coefficients are the same as the Beta coefficients and it helps in the direct comparison of the strength of one variable against another variable. It is possible to do a comparison of a Beta (standardized) coefficient against another standardized coefficient since they are determined in standard deviations. However with the unstandardized coefficients, it is impossible to give a direct comparison between two variables since these are not measured in standard deviations. Instead, it is only possible to state that a one unit change in the predictor variables results into a given unit change in the outcome variable (Siegel, 2011).

Confidence interval

The confidence interval (CI) for axin is 95% CI (-.083 – .000) indicating that the value of the regression coefficients in the population falls within -.083 and .000 (Table 7). The confidence intervals values produced for unstandardized regression coefficients are helpful in determining the likely value of the regression coefficients in the population.

Summary

From the above analyses and interpretations, it can be said that the more an individual is assertive, the less likely the individual is to hold anger “in.” In other words, assertive individuals tend to express anger more openly. Increased assertiveness leads to decreased tendency to hold anger in.

References
Field, A. (2009). Discovering statistics using SPSS. California, SAGE Publications Ltd.

Appendix
Table 1: Mean and SD for “rath” and “axout”

Descriptive Statistics

Mean
Std. Deviation
N

rath
3.3902
.43300
65

axout
2.1071
.42766
63

Table 2: Pearson Correlation for “rath” and “axout”

Correlations

rath
axout

rath
Pearson Correlation
1
.286*

Sig. (2-tailed)

.023

N
65
63

axout
Pearson Correlation
.286*
1

Sig. (2-tailed)
.023

N
63
63

*. Correlation is significant at the 0.05 level (2-tailed).

Table 3: Mean and Standard Deviation for Crowne-marlowe and Axin

Descriptive Statistics

Mean
Std. Deviation
N

crowne-marlowe
.6850
.07625
65

axin
2.2519
.44825
65

Table 4: Correlation between Crowne-marlowe and Axin

Correlations

crowne-marlowe
axin

Pearson Correlation
crowne-marlowe
1.000
-.246

axin
-.246
1.000

Sig. (1-tailed)
crowne-marlowe
.
.024

axin
.024
.

N
crowne-marlowe
65
65

axin
65
65

Variables Entered/Removedb

Model
Variables Entered
Variables Removed
Method

1
axina
.
Enter

All requested variables entered.
Dependent Variable: crowne-marlowe

Table 5: Regression Analysis

Model Summary

Model
R
R Square
Std. Error of the Estimate

1
.246a
.061
.046
.07448

Predictors: (Constant), axin

Table 6: ANOVA Test and F-Statistic

ANOVAb

Model
Sum of Squares
df
Mean Square
F
Sig.

1
Regression
.023
1
.023
4.073
.048a

Residual
.349
63
.006

Total
.372
64

Predictors: (Constant), axin
Dependent Variable: crowne-marlowe

Table 7: Unstandardized and Standardized Coefficients

Coefficientsa

Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
95.0% Confidence Interval for B

B
Std. Error
Beta
Lower Bound
Upper Bound

1
(Constant)
.779
.048

16.348
.000
.684
.875

axin
-.042
.021
-.246
-2.018
.048
-.083
.000

Dependent Variable: crowne-marlowe

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