Statistics | ANOVA | Assignment

Running head: STATISTICS 1
Statistics
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STATISTICS 2
Statistics
Introduction
The selected dataset is quantitative in nature hence can be easily prepared, explored,
analyze, presented and validated based on the variables. In addition, this type of dataset can be
analyzed using both descriptive and inferential statistics. The descriptive statistics are used to
describe and summarize the data in the form of frequencies, percentages, and means. The
inferential statistics, on the other hand, are used to help make inferences and draw conclusions.
Statistical test including variances, standard deviations, and ANOVA is also used to test the
hypothesized statements. All tests of significance can be computed at α = 0.05. Given that this is
a social science, setting alpha at 0.05 and a confidence level at 95% is ideal since it gives the best
assumption should the results be statistically significant.
Methodology
The design expert software has been used for the analysis. Both the descriptive and inferential
statistics including ANOVA, correlation and linear regression analysis have been presented. Four
factors; A, B, C and D have also been used.
Ressults
According to the results; the factor; C has the highest frequencies; 260 (89.7%). For factor B and
D, they have the same frequency distribution at 12 (4.1%) respectively. The lowest frequency is
6 (2.1%) for factor A.
Response Predicted
Mean
Predicted
Median* Observed Std Dev SE
Mean
95% CI
low for
Mean
95% CI
high for
Mean
95% TI
low for
99% Pop
95% TI
high for
99%
Pop
Factors† 12.0356 12.0356 0.00458216 N/A 12.0331 12.0381 12.0153 12.056
For the levels, High level (+1) is leading; 153 (52.8%) compared to the lowest level (-1); 137
(47.2%).
STEP I:
MODEL: LINEAR
Model Summary Statistics
Source Std. Dev. R² Adjusted R² Predicted R² PRESS
Linear 0.0000 0.9997 0.9996 0.9994 2.329E-08
2FI 7.996E-07 1.0000 1.0000 1.0000 3.274E-11 Suggested
Quadratic * Aliased
 Case(s) with leverage of 1.0000: PRESS statistic not defined.

STATISTICS 3
Focus on the model maximizing the Adjusted R² and the Predicted R².
The Model Summary table shows the multiple linear regression model summary and overall fit
statistics. It was found out that the adjusted R² of the model is 0.9996 with the R² = 0.9997 that
means that the linear regression explains 99.97% of the variance in the data. Due to the fact that
the differences between R square and Adjusted R square are small (0.0001) shows that the
independent variables were precise.
STEP II:
ANOVA
From the ANOVA table, it shows that all the independent variables which include; A, B, C, and
D do not help to predict the levels, (F= 9200, p- value < 0.05). This implies that the null
hypotheses were useless hence we reject the null hypotheses and reject the alternate hypotheses
of the independent variables. In other words, the test is not statistically significant hence can
assume that there is no linear relationship between the variables in the model.
STEP III:

STATISTICS 4
REGRESSION EQUATION
The linear regression model is specified as;
Where yi is Levels
β0 is a constant
β1x1 is A
β2x2 is B
β3x3 is C
β4x4 is D
The regression equation is, therefore, be specified as:
yi=0.083087-0.000287x1-0.000287x2- 0.001433x3-0.000287x4
From this equation, it shows that for every 3, there is likely to see a 2% change in levels.
STEP IV:
DIAGNOSTICS
According to the above table, the Beta weights indicate how the independent variables are of
importance as well as the collinearity statistics. Now that, there is only a single independent
variable in our analysis, there is no need to consider those values. However, from the findings in
the multiple regression, it shows that all the independent variables have predictive value for the
dependent variable meaning they are all statistically significant hence the null hypotheses are
rejected while accepting the alternate hypotheses since the p-value is less than 0.05.
From the Unstandardized Coefficients, the model predicts that change from one factor (-.023)
would result in a decrease in levels. On the other hand, Beta expresses the relative importance of
each independent variable in standardized terms. Firstly, the results show that all the independent
variables have a lower impact (beta = -.028). In conclusion, a multiple regression was run to
predict levels from the independent variables (A, B, C, D). These variables do not statistically
significantly predicted Levels. All four variables did not add statistically significantly to the
prediction, p > .05.
In addition, the table on Collinearity Diagnostics indicates that there are no multicollinearity
problems given that the eigenvalues are close to 0, indicating that the predictors are highly