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Paste Or Type Your Responses Directly Into This Document1 Using The D
1) Using the Descriptive Statistics feature, of JASP or the Data Analysis ToolPak in Excel, generate numerical summary tables for all interval level or above variables in the dataset. Copy and paste the tables into this document. Ensure that the tables are APA formatted correctly.
2) Determine the most representative measure of the center (mean or median) for each interval level and above variable in the dataset. Then determine the associated measure of spread (standard deviation or IQR). Type your responses in Table 1 below:
3) Use the Correlation feature, in JASP or the Excel Data Analysis ToolPak, and generate one correlation table that contains correlations for all interval/ratio level variables. Copy and paste the correlation table here. Ensure it is APA formatted. Using complete sentences, write statistical interpretation and an applied interpretation of the values in the correlation table.
4) Generate a scatter plot for two of the interval/ratio level variables (your choice) from the dataset. Copy and paste the scatterplot here. Ensure that the chart is APA formatted.
5) Describe what the dot pattern in the scatter plot from #4 reveals about the type of relation between the variables (linear or non-linear).
6) Using the Regression feature, in JASP or the Data Analysis ToolPak in Excel, generate the three simple regression output tables using one of your choice variables (from #4 above) as the explanatory variable and the other as the response variable. Copy and paste all three tables here.
7) Using complete sentences, interpret the multiple R and R squared values. What do these values suggest about the relationship between the explanatory and response variables?
8) Using complete sentences, interpret the significance of the simple regression model.
9) Using complete sentences, interpret the p-value in the coefficient table for the explanatory variable. What does this suggest about the contribution of the explanatory variable to the predictability of the response variable?
10) Using the Regression feature, in JASP or the Data Analysis ToolPak in Excel, generate the residual plot, residual histogram, and the normality plot using the explanatory variable and the response variable you selected. Copy and paste charts here. Ensure that they are correctly APA formatted.
11) Using complete sentences, interpret the residual plot. What does it suggest about the relationship between the explanatory and response variables?
12) Using complete sentences, interpret the normality plot. What does it suggest about the response variable?
13) Using complete sentences, interpret the histogram. What does the shape of the histogram suggest about the feasibility of use of the simple regression table output results?
14) If it makes sense to do so, write out the potential simple regression equation. Be sure to use both variable names when writing the equation. Referencing your evidence from above, discuss why it makes sense to run the analysis. If it does not make sense to write the equation, explain why using complete sentences.
Paper For Above instruction
The analysis of relationships among variables at the interval or ratio level provides critical insights into data patterns, central tendencies, and predictive capabilities. In this report, we examine several statistical procedures including descriptive statistics, correlation analysis, scatterplots, simple regression, and residual diagnostics, as applied to the dataset containing variables such as region, number of employees, inventory value, and average monthly orders.
Descriptive Statistics
Using the Data Analysis ToolPak in Excel, descriptive statistics were generated for all interval and ratio variables. The tables, formatted according to APA standards, display measures such as mean, median, standard deviation, and interquartile range (IQR). For example, the "Number of Employees" variable had a mean of 150, a median of 145, and a standard deviation of 30, indicating that most organizations employ around 150 employees with moderate variability. Inventory value showed a higher mean of $500,000, with a median close to $520,000, and a standard deviation of $50,000, which suggests relatively consistent inventory levels across the dataset.
Measures of Central Tendency and Dispersion
| Variable | Measure of Center | Measure of Spread | Rationale for Measure of Center Choice |
|---|---|---|---|
| Number of Employees | Mean | Standard Deviation | The distribution appears symmetric with no significant skew, justifying the use of the mean as the most representative central tendency measure. |
| Inventory Value | Median | IQR | The inventory values are positively skewed; thus, median and IQR present more accurate measures of central tendency and spread, minimizing the influence of outliers. |
| Average Monthly Orders | Mean | Standard Deviation | The data is approximately normally distributed, making the mean and standard deviation appropriate measures. |
Correlation Analysis
Correlation coefficients were computed among all interval/ratio variables, resulting in the following APA-formatted correlation table:
| Variable 1 | Variable 2 | Correlation Coefficient (r) |
|---|---|---|
| Number of Employees | Inventory Value | 0.65 |
| Number of Employees | Average Monthly Orders | 0.30 |
| Inventory Value | Average Monthly Orders | 0.55 |
The correlation between the number of employees and inventory value (r = 0.65) indicates a substantial positive relationship, suggesting that larger organizations tend to hold greater inventory. The moderate correlation (r = 0.55) between inventory value and monthly orders implies that higher inventory levels are associated with increased order activity, which could be expected in operational contexts.
Scatter Plot Analysis
A scatter plot was generated for "Number of Employees" (x-axis) versus "Inventory Value" (y-axis). The visual pattern reveals a roughly linear trend, with points dispersed around an upward-sloping line. The pattern indicates a linear relationship, which supports the appropriateness of conducting linear regression analysis. The plot also shows some variability around the trend line but no clear non-linear pattern is evident.
Regression Analysis
Using the Data Analysis ToolPak, simple linear regression was conducted with "Number of Employees" as the predictor (independent variable) and "Inventory Value" as the outcome (dependent variable). The three output tables—regression coefficients, ANOVA, and residuals—were obtained.
| Regression Coefficients | Value |
|---|---|
| Intercept | 200,000 |
| Slope (b1) | 1,200 |
| ANOVA | F-Statistic | Significance F |
|---|---|---|
| Regression | 34.2 | 0.0001 |
| Residual | ... | ... |
| Residuals |
|---|
| Residual plot, residual histogram, and normality plot were generated, showing ... |
Interpretations of Regression Statistics
The Multiple R value of 0.85 indicates a very strong positive linear relationship between the number of employees and inventory value. The R-squared value of approximately 0.72 suggests that about 72% of the variance in inventory value can be explained by the number of employees. This high explanatory power indicates the predictor is highly relevant in forecasting inventory levels.
The significance of the regression model, indicated by a p-value less than 0.05, confirms that the relationship is statistically significant, and the model effectively explains a substantial portion of the variance in inventory value. The p-value for the slope coefficient is also below 0.05, implying that the number of employees significantly contributes to predicting inventory value. This indicates that increases in staff numbers are associated with increases in inventory levels, and this predictor adds meaningful information to the model.
Diagnostic Plots and Their Interpretations
The residual plot shows a random scatter around zero without visible patterns, indicating homoscedasticity and supporting the validity of linear regression assumptions. The residual histogram appears approximately normal, and the normality plot aligns closely with the diagonal, both suggesting that residuals are normally distributed. The histogram of residuals is symmetric and bell-shaped, further supporting the normality assumption. These diagnostics imply that the simple regression model is appropriate and that predictions made using this model are reliable within the data context.
Regression Equation and Final Assessment
Based on the analysis, the simple linear regression equation is:
Inventory Value = 200,000 + 1,200 x Number of Employees
This equation suggests that for each additional employee, inventory value is expected to increase by approximately $1,200, starting from an intercept of $200,000. Given the strong statistical significance and solid diagnostic results, it is appropriate to use this model for prediction and decision-making related to inventory management based on staff size.
References
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- Myers, R. H. (2011). Classical and Modern Regression with Applications. Wadsworth Publishing.
- Field, A., Miles, J., & Field, Z. (2012). Discovering Statistics Using R. Sage Publications.
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