Unit VII Research Paper Research Methods
1
4
Jovan Maires
Columbia Southern University
Research Methods
Dr. Renee Norris-Jones
19 September 2022
Data Analysis: Hypothesis Testing
Correlation: Hypothesis Testing
Ho1: The sample data are not significantly different from a normal
Ha1: The sample data are significantly different from a normal population.
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.715984 |
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R Square |
0.512633 |
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Adjusted R Square |
0.507808 |
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Standard Error |
1.819898 |
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Observations |
103 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
351.8572 |
351.8572 |
106.2362 |
1.89E-17 |
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Residual |
101 |
334.5148 |
3.312028 |
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Total |
102 |
686.372 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
12.65058 |
0.70179 |
18.02616 |
2.47E-33 |
11.25842 |
14.04274 |
11.25842 |
14.04274 |
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X Variable 1 |
-0.98135 |
0.095211 |
-10.3071 |
1.89E-17 |
-1.17022 |
-0.79248 |
-1.17022 |
-0.79248 |
R = 0.715984185
R2 = 0.5126
P =0.00247
The Pearson correlation coefficient of r = 0.715984185, implies a moderately strong positive correlation. This corresponds to R2 of 51 percent of the variance between the variables.
Applying an alpha of 0.05, the results show that a p-value of 0.00247 < 0.05, Therefore, the null hypothesis is rejected, and the alternative hypothesis is accepted that there is a statistically significant link between the variables (Bugni & Canay, 2021).
Simple Regression: Hypothesis Testing
Ho2: There is a statistically significant relationship between the expenditure and the lost time
Ha2: There is no statistically significant relationship between the expenditure and the lost time
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.915447 |
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R Square |
0.838043 |
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Adjusted R Square |
0.83644 |
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Standard Error |
148.3451 |
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Observations |
103 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
11500980 |
11500980 |
522.6227 |
1.03E-41 |
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Residual |
101 |
2222634 |
22006.28 |
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Total |
102 |
13723614 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
1981.468 |
45.00229 |
44.03037 |
9.88E-68 |
1892.195 |
2070.74 |
1892.195 |
2070.74 |
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X Variable 1 |
-7.73009 |
0.338135 |
-22.8609 |
1.03E-41 |
-8.40086 |
-7.05932 |
-8.40086 |
-7.05932 |
R = 0.915447
R2 = 0.838043
P =0.00103
Annova f value = 522.6227
The Pearson correlation coefficient of r = 0.915447, implies a strong positive correlation. This corresponds to R2 of 83 percent of the variance between the variables.
Applying an alpha of 0.05, the results show a p-value of 0.00103 < 0.05, and ANOVA f value of 522. 6227. Therefore, the null hypothesis is rejected, and the alternative hypothesis is accepted that there is a statistically significant link between the variables.
Multiple Regression: Hypothesis Testing
Ho3: There is a statistically significant relationship between the frequency and the decibel
Ha3: There is no statistically significant relationship between the frequency and the decibel
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.390711 |
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R Square |
0.152655 |
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Adjusted R Square |
0.152091 |
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Standard Error |
2902.952 |
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Observations |
1503 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
2.28E+09 |
2.28E+09 |
270.4163 |
5.36E-56 |
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Residual |
1501 |
1.26E+10 |
8427129 |
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Total |
1502 |
1.49E+10 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
25175.68 |
1357.506 |
18.54554 |
2.7E-69 |
22512.87 |
27838.49 |
22512.87 |
27838.49 |
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X Variable 1 |
-178.549 |
10.85776 |
-16.4443 |
5.36E-56 |
-199.847 |
-157.251 |
-199.847 |
-157.251 |
R = 0.39071
R2 = 0.152
P = 0.0027
Annova f value = 270.4163
The Pearson correlation coefficient of r = 0.39071, implies a strong negative correlation. This corresponds to R2 of 15 percent of the variance between the variables.
Applying an alpha of 0.05, the results show that a p-value of 0.0027 < 0.05, a and Annova f value of 270.4163 (Nicholson et al, 2021). Therefore, the null hypothesis is accepted, and the alternative hypothesis is accepted that there is a statistically significant link between the variables.
References
Bugni, F. A., & Canay, I. A. (2021). Testing continuity of a density via g-order statistics in the regression discontinuity design. Journal of Econometrics, 221(1), 138-159.
Nicholson, K. J., Reyes, A. A., Sherman, M., Divi, S. N., & Vaccaro, A. R. (2021). Power analysis for null hypothesis significance testing. Clinical spine surgery, 34(2), 63-65.