Introduction Before moving into a new neighborhood, there are many indexes people need to take into consideration, for instance, the crime rates, the quality of the educational institutions in the neighborhood as well as other neighborhood welfares. It is common for people who have children to move to districts with great educational services. On the contrary, people who do not have children will move out of these neighborhoods to avoid additional fees. Sometimes. These factors which affect people decisions to stay in or move out of the neighborhood interest me. This project will study the correlations between the population of Denver neighborhoods and 6 possible factors. The dataset was gathered from 45 Denver neighborhoods. And I will …show more content…
Then I run a Fit Regression Model with x3, x6 and x7. Then I test the significance of the regression line. To test the significance of the coefficients: H0: βk = 0 (k=3, 6, 7); H1: at least one of these coefficients does not equal to 0. F= [∑ (ŷi- ȳ) /p] / σ^2 = MSR/MSE = 3.56 with p-value = 0.02 < 0.05; σ^2 = ∑ (Yi - ŷi) ^2 / (n-p-1) = 426.61. The F value is statistically significant. Therefore, we have the sufficient evidences reject the null hypothesis. To test the significance of the intercept:H0: β0=0; H1: β0≠0. t (n-4) = ^β0- β0 / SE (^β0) = 2.89; p-value = 0.006 <0.05. The t-score is statistically significant. Therefore, we have sufficient evidence to reject the null hypothesis. To test the significance of other coefficients. H0: βk=0; H1: βk≠0. K= (3,6,7) t (n-4) = ^β3- β3 / SE (^β3) = (0.0631-0)/ 2.05 = 2.89 with p-value = 0.308; t (n-4) = ^β6- β6 / SE (^β6) = (-0.01325 - 0)/ 0.00502= -2.64 with p-value = 0.0128*; t (n-4) = ^β7- β7 / SE (^β7) = (-0.0605 -0)/ 0.0298= -2.03 with p-value= 0.049* The t-score is statistically significant for β6 and β7. Therefore, we have sufficient evidence to reject the null hypothesis for β6 and β7. However, the t-score is not statistically significant for β3. Therefore, we fail to reject the null hypothesis of β3. Then I run 4 residual plots for the regression. From the normal probability plot, the residuals fall along the
From the above output, we can see that the p-value is 0.000186, which is smaller than 0.05 (if we select a 0.05 significance level).
All the p-values are greater than 0.05, therefore there is a statistical difference between each transect.
15 In testing the hypotheses: H0 β1 ’ 0: vs. H1: β 1 ≠ 0 , the following statistics are available: n = 10, b0 = 1.8, b1 = 2.45, and Sb1= 1.20. The value of the test statistic is:
We reject Ho if χ2 > χα2. At α=0.05, with 4 degrees of freedom, the critical value becomes χα2=9.488 (table E.4)
Because the p-value of .035 is less than the significance level of .05, I will reject the null hypothesis at 5% level.
The statistical significance of a coefficient tests determines coefficients potential of being zero. The zero potential increases when there is significant variance in the independent variables. A large variance also suggests that the variable used have no effect on the dependent variable.
It tells that the t-statistic with 97 degrees of freedom was 2.14, and the corresponding p-value was less than .05, specifically around 0.035. Therefore, it is appropriate to conclude the research study was statistically significant.
To test the null hypothesis, if the P-Value of the test is less than 0.05 I will reject the null hypothesis.
However, treatment four, 0.1296 (±0.608), represents that the mean was extraneous from what it should be (Table 1). The t-tests show how different the mean is in each treatment.
We conduct an independent sample t-test using Excel, and obtain the following output (see sheet T-TEST)
All data in the figures are expressed as the mean ± 1 SD of proportions calculated from three independent experiments where each experimental condition was tested in triplicates. Significant differences were estimated using an ANOVA test as implemented in GraphPad Prism (Version 3.02 for Windows, GraphPad Software. San Diego, California. USA). The proportions were Arcsin-transformed to ensure normality of residuals prior to statistical analysis, and p-value thresholds for significance were adjusted using the Bonferroni correction (29) for multiple comparisons.
| Based on explicit knowledge and this can be easy and fast to capture and analyse.Results can be generalised to larger populationsCan be repeated – therefore good test re-test reliability and validityStatistical analyses and interpretation are
With a P-value of 0.00, we have a strong level of significance. No additional information is needed to ensure that the data given is accurate.
As stated above for the p-value, I was able to perform a hypothesis test for the regression coefficients of β₁, β₂, β₃. The coefficients of β₁, β₂, β₃ are the same as x₁, x₂, and x₃. This was examined by looking at the individual p-values to verify if these coefficients will be used in the model for explanation.
SUMMARY OUTPUT | | | | | | | | | | | | | | | | | | |Regression Statistics | | | | | | | | |Multiple R |0.984835305 | | | | | | | | |R Square |0.969900578 | | | | | | | | |Adjusted R Square |0.967164267 | | | | | | | | |Standard Error |473.2824687 | | | | | | | | |Observations |13 | | | | | | | | | | | | | | | | | | |ANOVA | | | | | | | | | | |df |SS |MS |F |Significance F | | | | |Regression |1 |79396723.52 |79396723.52 |354.455521 |1.02108E-09 | | | | |Residual |11 |2463959.247 |223996.2952 | | | | | | |Total |12 |81860682.77 | | | | | | | | | | | | | | | | | | |Coefficients |Standard Error |t Stat |P-value |Lower 95% |Upper 95% |Lower 95.0% |Upper 95.0% | |Intercept |4679.884615 |278.4549858 |16.80661096 |3.42384E-09 |4067.009324 |5292.759906 |4067.009324