ESSAY INSTRUCTIONS
Assignment Topic: Emotional Intelligence and EmpathyFormat: APA
This assignment consists of two parts. You must complete both parts and present them in one document. Each part of the assessment will present you with a description of a study and a partial data set. You will need to follow the instructions to add the final data points from completing a task or questionnaire using PsyToolKit. Once you have completed the data set, you will need to enter the data into SPSS and identify the appropriate statistical test to address the hypothesis. You will then write a results and discussion section of an APA style research report.
For each part of the assessment, please present the report, reference list, and appendix items together. This means you would present everything for part one and then everything for part two, all in one document.
For further details, see the description of each part below. Part one – Emotional Intelligence and Empathy
In order to complete this part, you will need to complete two questionnaires on PsyToolKit. Step one – please click this link to complete the Emotional Intelligence Scale
(Schutte et al., 1998): https://www.psytoolkit.org/survey-library/emotionalintelligence.html
To run the questionnaire, please click “Click here to run a demo of the survey”. Read the instructions to take part. Please make a note of your results and insert your data into the table below.
Step two – please click this link to complete the Empathy Quotient scale (Lawrence et al., 2004): https://www.psytoolkit.org/survey-library/empathy-arc.html
To run the questionnaire, please click “Click here to run a demo of the survey”. Read the instructions to take part. Please make a note of your results and insert your data into the table below.
The scores for each questionnaire per participant are shown in Table 1.
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Table 1.
Partial data set from 19 participants for both questionnaires. You need to complete the questionnaires yourself to add the 20th row of data
Participant Emotional
Intelligence Empathy
The hypothesis is that there will be a positive correlation between participants scores on the Emotional Intelligence scale and the Empathy Quotient scale.
Having gathered your own data, enter all the data into SPSS and apply an appropriate statistical test to the data to address the hypothesis. You should include an appropriate graph to visualise the results (you can use SPSS or Excel to make this).
Please write a report of your analysis to include only the Results, Discussion and References section of a report. Do not include an Introduction or Method Section.
For the results section, you will need to report the descriptive statistics, outcome of your checks of parametric assumptions and then the results of the inferential test
you select based on the design and whether the parametric assumptions are met.
Your lesson content discusses parametric assumptions along with the additional guide videos on the module. For guidance on presenting a results section in APA style, please see lesson 10.
For the Discussion section, you will need to read about relevant issues in order to interpret the data and compare the findings to previous research on the topic. You will also need to evaluate the method used in this study.
Further details on presenting both sections will be available in Live session 4 (slides will be available prior to the session).
Referencing
Please cite at least four relevant published articles in your discussion. Please do not use quotes in your report.
Appendix
Please supply two appendix items:
Appendix A: Raw Data. Please copy your own data into the table. This is the data shown on the previous page of the assignment brief with your scores as the 20th case.
Appendix B: SPSS Output. The Appendix will not be marked separately but your lecturer will refer to it when appraising your analysis in the Results section of your report.
References:
Lawrence, E. J., Shaw, P., Baker, D., Baron-Cohen, S., & David, A. S. (2004).
Measuring Empathy – reliability and validity of the empathy quotient. Psychological Medicine, 34, 911-919.
Baron-Cohen, S. & Wheelwright, S. (2004). The Empathy Quotient (EQ). An investigation of adults with Asperger Syndrome or High Functioning Autism, and normal sex differences. Journal of Autism and Developmental Disorders, 34, 163-175.
Schutte, N. S., Malouff, J. M., Hall, L. E., Haggerty, D. J., Cooper, J. T., Golden, C. J.,& Dornheim, L. (1998). Development and validation of a measure of emotional intelligence. Personality and Individual Differences, 25, 167–177
Part two – Mental Rotation Task
In order to complete this task, please click this link to take part in the Mental Rotation task using PsyToolKit:
https://www.psytoolkit.org/experiment-library/mentalrotation.html
To run the experiment, please click “Click here to run a demo”. Read the instructions to take part. Please make a note of your results for the mean response time and insert your data into the table below for your relevant biological sex. The mean response times made by each participant based on biological sex are shown in Table 2.
Table 2.
Partial data set from 19 participants for both conditions of the Mental Rotation task.
You need to complete the task yourself to add the 20th row of data. Do not worry that this will lead to uneven participant numbers in each group
Participant Male Female The hypothesis for this study is that there will be a difference between the two conditions, with males having faster response times than females
Having gathered your own data, enter all the data into SPSS and apply an appropriate statistical test to the data to address the hypothesis. You should include an appropriate graph to visualise the results (you can use SPSS or Excel to make this).
Please write a report of your analysis to include only the Results, Discussion and References section of a report. Do not include an Introduction or Method Section.
For the results section, you will need to report the descriptive statistics, outcome of your checks of parametric assumptions and then the results of the inferential test you select based on the design and whether the parametric assumptions are met.
Your lesson content discusses parametric assumptions along with the additional guide videos on the module. For guidance on presenting a results section in APA style, please see lesson 10.
For the Discussion section, you will need to read about relevant issues in order to interpret the data and compare the findings to previous research on the topic. You will also need to evaluate the method used in this study.
Further details on presenting both sections will be available in Live session 4 (slides will be available prior to the session).
Referencing
Please cite at least four relevant published articles in your discussion. Please do not use quotes in your report.
Appendix
Please supply two appendix items: Appendix A: Raw Data. Please copy your own data into the table. This is the data shown on the previous page of the assignment brief with your scores as the 20th case.
Appendix B: SPSS Output. The Appendix will not be marked separately but your lecturer will refer to it when appraising your analysis in the Results section of your report.
References:
Shephard, R.N. and Metzler, J. (1971). Mental Rotation of Three-Dimensional Objects. Science, 171, 701-703.
Collins, D.W. and Kimura, D. (1997). A Large Sex Difference on a Two-Dimensional Mental Rotation Task. Behavioral Neuroscience, 111, 845-849.
ESSAY WRITTEN SOLUTION
The first study was conducted to determine if there will be a positive correlation between the participant’s scores on the emotional intelligence scale and the empathy quotient scale. This descriptive study used two variables, including emotional intelligence and empathy. From the findings, it was clear that the scores for emotional intelligence ranged from between 145 and 100, with a range of 45. The study also showed that the scores for empathy quotient ranged from 74 to 25 with a range of 49. The average score for the emotional intelligence test was 127.3, and the average for emotional quotient was 49.45.
The most appearing or frequent score for emotional intelligence is 123, and the most frequent score for empathy quotient is 34. The data collected from emotional intelligence is negatively skewed by -0.6245, asymmetric distribution. In contrast, the data collected for the empathy quotient is positively skewed by 0.2099, which is symmetric. Also, the emotional intelligence data has a positive kurtosis of 0.309625 which means that it has a heavier tail when compared to the normal distribution. Data collected for the empath quotient has a negative kurtosis of -1.1687.
A correlation test was conducted to test the significance of the null hypothesis. The results showed a positive correlation between the participants’ scores regarding their emotional intelligence and empathy quotient by o.759254. Since the p-value observed is less than 0.05, we reject the null hypothesis and conclude that there is no significant correlation between the emotional intelligence and the empathy quotient scale. There is also linearity between the data because there is a positive coefficient between the variables. The t statistics have also been shown to be high, and therefore the groups are said to be different. That means that increased emotional intelligence would increase the empathy quotient (Fernández-Abascal & Martín-Díaz, 2019).
A regression analysis was conducted on the available data, so checking the model’s goodness of fit was necessary. Hypothesis testing was done to determine this factor, and in this case, the null hypothesis was model is not significant, and the alternative hypothesis was that the model is essential. From the analysis of variance calculations, the p-value was 2.43e-12, which means that it is less than the significance level, which was 0.05. This finding fails to reject the null hypothesis and conclude that the fitted model is significant. The following analysis was conducted on the coefficient of determination (R squared).
The R squared obtained from this analysis was 0.5765, which means that 57.65 percent of the emotional intelligence data is explained by the values gotten from the empathy quotient. The next step was to determine if the empath quotient significantly predicts a person’s emotional intelligence. This analysis required that hypothesis testing be done where the null hypothesis was empath quotient was not a significant predictor, and the alternative hypothesis was it is an important predictor. Since the p-value for the empath quotient was 0.0001, which is smaller than the significance level, we fail to reject the null hypothesis and conclude that the empathy quotient is a significant predictor.
It is also worth noting that the coefficient of the emotional quotient is positive by 0.57736, which means that a unit increase in the empathy quotient would increase the emotional intelligence by 0.57736.since the F statistic calculated is more significant than the F tabulated, we fail to reject the null hypothesis and conclude that the fitted model is substantial. The next step was to calculate the various model assumptions, including normality of the residuals, homogeneity of the variables, linearity, multicollinearity, and independence of the residuals (Uttley, 2019).
To test for linearity, a QQ-plot was constructed to check whether the point would form a straight line to show linearity. The results were that most of the variables joined together to form a straight line, and therefore the linearity test was positive. It is also evident from the fitted model that the returned equation was for a linear model. That means that you can use the emotional quotient to predict a person’s emotional intelligence using the fitted model. To test for normality, hypothesis testing needed to be done.
The hypothesis testing for normality had the null hypothesis as residuals with a normal distribution and an alternative distribution that the residuals were not typical in distribution. The Shapiro Wilk test was conducted, and the output was recorded. From this Shapiro test, the p-value got was seen to be 0.6033, more significant than the significance level, which was 0.05. Therefore, we reject the null hypothesis and conclude that the residuals have a normal distribution. The residuals tested here were obtained from the variance analysis conducted in the previous steps.
The following parametric assumption to be tested was the homogeneity of the variables, which is done by testing whether the residuals’ variance is constant. Therefore, hypothesis testing was conducted on the variance of the residuals. The null hypothesis is that the variance of the residuals is constant, and the alternative hypothesis is that the variance is not consistent. A test known as the Breusch-pagan test was used to this effect, and the p-value returned was 0.3623. Therefore, since the p-value gotten is greater than the significance value of 0.05, we fail to reject the null hypothesis and conclude that the variance of the residuals is constant (homoscedasticity).
Another assumption tested is the independence of the residuals which is done by checking if there is autocorrelation between the residuals. Therefore, just like all the other parametric assumptions, hypothesis testing must be conducted to determine if there is autocorrelation or not. A test known as the Durbin Watson test was completed, and the p-value obtained was 0.48. Since the p-value obtained is more significant than the significance level used, which is 0.05, we fail to reject the null hypothesis and conclude autocorrelation between the residuals.
The study, therefore, concluded that there was a direct relationship between empathy quotient and emotional intelligence and that there was a correlation between the variables. The regression equation for the model would be y= -78.487 + 1.005 X, whereby y would be emotional intelligence and X would be the empathy quotient. The graph also demonstrated a positive correlation, with the chart being on the positive side and moving upwards.
From the findings above and the discussions of what the results meant, it was evident that the empath quotient of a person affects their emotional intelligence. Emotional intelligence is usually the skill that allows you to understand the thoughts and behavior of human beings. To do that, you need to feel and understand the feelings and emotions of others and become an empath. Therefore, this result means that if you have a high emotional quotient, you are most likely to have high emotional intelligence and vice versa. This information is helpful because it can help you improve your emotional intelligence.
Several tests have been developed to help test the empath quotient of a person, just like the one done in this study to come up with the data to perform it. From the fitted model equation, the intercept came back positive, which is why there is a direct relationship between emotional intelligence and the empath quotient. One similar study investigated intelligence quotient and emotional intelligence among Saudi business students towards academic performance (Khan, 2018).
This study was done to understand the most dominant form of intelligence that affects the performance of undergraduate business students. The investigators analyzed the most essential factors influencing emotional intelligence and IQ to achieve this. The results showed that memory, self-awareness, and empathy were the main predictors of how a person was emotionally intelligent or how high their IQ was. Conducting this study was necessary because it helped determine areas that needed improvement to improve the students’ performance. It also demonstrated the importance of emotional intelligence regarding a person’s performance either in life or in school.
From this study, some of the limitations were that the data collected was only restricted to two variables, making it challenging to be sure to what extent the empath quotient factor is compared to other factors (Korkman & Tekel, 2020). The study also relied on questionnaires as a data source that can be easily altered to suit a particular case. Therefore, the data collected from questionnaires is restrictive because the choices were restricted only to the answers given. However, there is a need for further research to focus on other factors like age, mental condition, and so much more.
References
Fernández-Abascal, E. G., & Martín-Díaz, M. D. (2019). Relations between dimensions of emotional intelligence, specific aspects of empathy, and non-verbal sensitivity. Frontiers in psychology, 10, 1066.
Uttley, J. (2019). Power analysis, sample size, and assessment of statistical assumptions—Improving the evidential value of lighting research. Leukos.
Khan, S. (2018). Demystifying the impact of university graduate’s core competencies on work performance: A Saudi industrial perspective. International Journal of Engineering Business Management, 10, 1847979018810043.
Korkman, H., & Tekel, E. (2020). Mediating Role of Empathy in the Relationship between Emotional Intelligence and Thinking Styles. International Journal of Contemporary Educational Research, 7(1), 192-200.
Appendix A
The emotional intelligence score was 124, and the empathy quotient score was 43 for the first study table.
Appendix B
Column1 | Column2 | ||
Mean | 127.3 | Mean | 49.45 |
Standard Error | 2.522634 | Standard Error | 3.339142 |
Median | 127.5 | Median | 47 |
Mode | 123 | Mode | 34 |
Standard Deviation | 11.28156 | Standard Deviation | 14.9331 |
Sample Variance | 127.2737 | Sample Variance | 222.9974 |
Kurtosis | 0.309625 | Kurtosis | -1.1687 |
Skewness | -0.62456 | Skewness | 0.209984 |
Range | 45 | Range | 49 |
Minimum | 100 | Minimum | 25 |
Maximum | 145 | Maximum | 74 |
Sum | 2546 | Sum | 989 |
Count | 20 | Count | 20 |
Confidence Level(95.0%) | 5.279934 | Confidence Level(95.0%) | 6.988904 |
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 1394.012 | 1394.012 | 24.49961 | 0.000104 | |||
Residual | 18 | 1024.188 | 56.89935 | |||||
Total | 19 | 2418.2 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 98.93565 | 5.973584 | 16.56219 | 2.43E-12 | 86.38561 | 111.4857 | 86.38561 | 111.4857 |
X Variable 1 | 0.573597 | 0.115885 | 4.949708 | 0.000104 | 0.330131 | 0.817062 | 0.330131 | 0.817062 |
SUMMARY OUTPUT | |
Regression Statistics | |
Multiple R | 0.759254 |
R Square | 0.576467 |
Adjusted R Square | 0.552937 |
Standard Error | 9.984681 |
Observations | 20 |
Shapiro-Wilk normality test
W = 0.9629, p-value = 0.6033
Breusch-Pagan test
BP = 0.82996, df = 1, p-value = 0.3623
durbinWatsonTest(model)
lag Autocorrelation D-W Statistic p-value
1 0.1106573 1.746616 0.474
Alternative hypothesis: rho != 0
The second study was conducted to determine if there will be a difference between the two conditions, the males having a faster response than females. The null hypothesis, in this case, would be the former in that statement, and the alternative hypothesis would be that there is no difference between the two conditions. This study was mainly descriptive, and the descriptive statistics analysis showed that males had a range between 1815 and 2785 with a range of 974. On the other hand, women ranged from 1876 and 2891 with 1015. From the fitted linear regression model, it was evident that there is an indirect relationship between the two variables (Mishra et al., 2019).
From the data gotten, it was observed that the average number of males was 2156.05, and the average number of females was 2313. The most frequent number of male rotation times is 2234, and that of the female is not available because they each have different time frames. The data collected for the males is positively skewed by 1.15622, which means that the data is symmetric, while that of females is also positively skewed by 0.3666, which means that it is also symmetric. From the study, it was also evident that the data for males have a positive kurtosis, which means that it has a heavier tail than a normal distribution. The data collected for females had a negative kurtosis, which meant a lighter seat.
A regression analysis was conducted on this data to figure out if the model used to analyze this data is significant or not. Therefore, hypothesis testing was born with the null hypothesis as the model is not substantial and the alternate hypothesis is substantial. The p-value obtained from the analysis was 0.6515, which is bigger than the significance level, which is 0.05. Therefore, we reject the null hypothesis and conclude that the model is insignificant for this data. The subsequent analysis will be to check for the coefficient of determination (R squared) to determine the relationship of the variables.
The coefficient of determination returned by the analysis was o.o1158, which means that only 1.158 percent of the male mental rotation time is explained by the female mental rotation time. This percentage is achieved by multiplying the R squared coefficient by 100. The subsequent analysis performed was to determine if the female rotation time was a significant predictor of the male rotation time. Hypothesis testing was conducted with the null hypothesis as female time is not a substantial predictor and alternate hypothesis vice versa. The p-value obtained was 0.652, which is greater than 0.05. Therefore, we fail to reject the null hypothesis and conclude that the female mental rotation time is not a significant predictor of the male mental rotation time.
In addition, the coefficient of female mental time rotation is -0.0923, which means that a unit increase in the female mental rotation time increases the male mental rotation time by -0.0923. The F statistic was also obtained to help determine the significance of the used model. The F statistic returned as 0.2109, less than the tabulated F statistic. Therefore, we reject the null hypothesis and conclude that the fitted model is insignificant. The next step was the analysis of the parametric assumptions that were made while conducting this study. These parametric assumptions include linearity, normality of the residuals, homogeneity, and independence of the residuals.
The first assumption was that there was the linearity of the data used. From the tests conducted and the graphs plotted during the analysis, the data showed no linearity. The data points used to plot the data were not linear enough to devise a straight line, and the fitted model equation brings back not linear data points. The normality of the residuals was then investigated as part of the assumptions made when choosing the model.
To test for the normality of the residuals, hypothesis testing was conducted with the null hypothesis as the residuals have a normal distribution and an alternate hypothesis as the residuals are not normal in distribution. To help perform this investigation, a test known as the Shapiro Wilk test is used. When the test was performed on the data, the p-value observed was 0.08774, more significant than the significance level. Therefore, we reject the null hypothesis and conclude that the residuals have a normal distribution. The residuals were calculated from the analysis of the variance test.
The homogeneity of the variables was another parametric assumption that was analyzed. This analysis was done through hypothesis testing with a null hypothesis as the variance of the residuals is constant, and the alternate hypothesis as the variance is not a constant. A test known as the Breusch-pagan test was used to this effect, and it returned a p-value of 0.3489. Therefore, this means that since the p-value is more significant than the significance level, we fail to reject the null hypothesis and conclude that the variance of the residuals is constant (homoscedasticity). The following assumption to be tested is the independence of the residuals.
The independence of the residuals is usually done to test whether there is autocorrelation between the residuals or not. As usual, hypothesis testing was conducted with the null hypothesis as there is autocorrelation between the residuals and the alternate hypothesis as there is no autocorrelation between the residuals. A test known as the Durbin Watson test was used, and it brought back a p-value of 0.548. The p-value observed is more significant than the significance level, and therefore we fail to reject the null hypothesis and conclude that there is autocorrelation between the residuals. The multicollinearity assumption could not be tested because the data frame consisted of only two variables.
A test for the significance of the model was conducted on the null hypothesis to determine whether to reject or accept it. The p-value was 0.6, more significant than 0.05; we get the idea and conclude that there is a difference between males and females, with the males having a faster response. The r squared value is 0.5, a weak or small effect size. There is also linearity between the variables’ data because there is a negative coefficient. The variables are also correlated because multiple regression R brought back a positive figure of 0.1076 (Kim & Park, 2019).
The graph also shows a positive relationship because it is on the positive side of the integers. Therefore, the fitted linear regression equation becomes Y= 2369.60958 – 0.0923042 X, where Y is the number for Males and X is females. Since the intercept is positive, then that means that there is a direct relationship between the variables. The study’s objective was to establish if there will be a difference between the two conditions, whether the males are faster in terms of response than the males. From the findings, it was evident that there is a difference between the two conditions; however, the study showed that males had a faster response rate than women according to their p-value difference. (Astivia & Zumbo, 2019).
Mental rotation is usually tough to monitor because people have different ways of performing and interpreting a particular situation. It is usually an essential thing to do because it helps make someone understand a specific situation better. You cannot know how it feels to be a woman or a man unless you put yourself in their shoes. That is why this study was conducted to determine the difference in how men and women perceived a particular situation. Since it was determined that there was a difference in how they perceived things, with men having a faster response rate than men, it helps women understand that men have a better judgment of things when it comes to various situations.
A similar study conducted by the department of psychology at Emory University to find out if there is a difference between mental rotations and object preference in early sex gave back similar results. The study showed that male infants had a higher mental rotation performance than female infants. However, even though the males performed better than females in terms of mental rotation tasks, the distributions overlapped significantly, which shows the similarities in the preference of individuals that comprise the performance of both sexes. This indicates that there is a difference that occurs from birth and during the entire lifespan of both males and females.
The study, however, has the limitation that the data only comprises one factor instead of several factors to determine how the difference in mental rotation relates to other factors. Also, the data collected could be restricted or biased because the choices offered are confined to specific situations only. This means that there is a need to consider open-ended questions to remove the aspect of being biased or restrictions that have been imposed. This can help better investigate the main differences that exist when it comes to male and female mental capabilities. It is this factor that determines how well we perceive the things that occur in our day to day lives.
References
Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of cardiac anesthesia, 22(1), 67.
Kim, T. K., & Park, J. H. (2019). More about the basic assumptions of t-test: normality and sample size. Korean Journal of anesthesiology, 72(4), 331.
Astivia, O. L. O., & Zumbo, B. D. (2019). Heteroskedasticity in Multiple Regression Analysis: What it is, How to Detect it and How to Solve it with Applications in R and SPSS. Practical Assessment, Research, and Evaluation, 24(1), 1.
Constantinescu, M., Moore, D. S., Johnson, S. P., & Hines, M. (2018). Early contributions to infants’ mental rotation abilities. Developmental Science, 21(4), e12613
Appendix A
For the second study table, the score for the mental rotation time for male was is 1998 and female is 2003.
Appendix B
Column1 | Column2 | ||
Mean | 2156.05 | Mean | 2313.65 |
Standard Error | 56.96026 | Standard Error | 66.4139 |
Median | 2101 | Median | 2340.5 |
Mode | 2234 | Mode | #N/A |
Standard Deviation | 254.734 | Standard Deviation | 297.012 |
Sample Variance | 64889.42 | Sample Variance | 88216.13 |
Kurtosis | 1.31408 | Kurtosis | -0.47043 |
Skewness | 1.156229 | Skewness | 0.366617 |
Range | 974 | Range | 1015 |
Minimum | 1815 | Minimum | 1876 |
Maximum | 2789 | Maximum | 2891 |
Sum | 43121 | Sum | 46273 |
Count | 20 | Count | 20 |
Confidence Level(95.0%) | 119.2192 | Confidence Level(95.0%) | 139.0059 |
Regression Statistics | ||||||||
Multiple R | 0.107624 | |||||||
R Square | 0.011583 | |||||||
Adjusted R Square | -0.04333 | |||||||
Standard Error | 260.1942 | |||||||
Observations | 20 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 14280.53 | 14280.53 | 0.210935 | 0.651533 | |||
Residual | 18 | 1218618 | 67701.02 | |||||
Total | 19 | 1232899 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 2369.61 | 468.6167 | 5.056605 | 8.21E-05 | 1385.082 | 3354.137 | 1385.082 | 3354.137 |
X Variable 1 | -0.0923 | 0.200977 | -0.45928 | 0.651533 | -0.51454 | 0.329933 | -0.51454 | 0.329933 |
RESIDUAL OUTPUT | PROBABILITY OUTPUT | |||||||
Observation | Predicted Y | Residuals | Standard Residuals | Percentile | Y | |||
1 | 2162.387 | 71.61332 | 0.282772 | 2.5 | 1815 | |||
2 | 2139.864 | 16.13554 | 0.063713 | 7.5 | 1842 | |||
3 | 2153.71 | 635.2899 | 2.508505 | 12.5 | 1914 | |||
4 | 2142.91 | -155.91 | -0.61563 | 17.5 | 1986 | |||
5 | 2153.156 | -311.156 | -1.22863 | 22.5 | 1987 | |||
6 | 2186.201 | -143.201 | -0.56544 | 27.5 | 1990 | |||
7 | 2181.863 | -92.8629 | -0.36668 | 32.5 | 1998 | |||
8 | 2124.727 | 109.2734 | 0.431477 | 37.5 | 2013 | |||
9 | 2140.88 | -226.88 | -0.89586 | 42.5 | 2043 | |||
10 | 2174.571 | -359.571 | -1.4198 | 47.5 | 2089 | |||
11 | 2145.218 | 199.7819 | 0.788858 | 52.5 | 2113 | |||
12 | 2135.803 | 175.1969 | 0.691782 | 57.5 | 2156 | |||
13 | 2153.433 | -163.433 | -0.64533 | 62.5 | 2215 | |||
14 | 2104.05 | 110.9496 | 0.438095 | 67.5 | 2234 | |||
15 | 2196.447 | 505.5531 | 1.996226 | 72.5 | 2234 | |||
16 | 2194.878 | 150.1222 | 0.592772 | 77.5 | 2311 | |||
17 | 2179.832 | -66.8322 | -0.26389 | 82.5 | 2345 | |||
18 | 2163.587 | -177.587 | -0.70122 | 87.5 | 2345 | |||
19 | 2102.758 | -89.7582 | -0.35442 | 92.5 | 2702 | |||
20 | 2184.724 | -186.724 | -0.7373 | 97.5 | 2789 |
Shapiro-Wilk normality test
W = 0.91725, p-value = 0.08774
Breusch-Pagan test
BP = 0.8775, df = 1, p-value = 0.3489
DurbinWatsonTest
lag Autocorrelation D-W Statistic p-value
1 0.1216846 1.723811 0.512
Alternative hypothesis: rho != 0