Performing Regression Analysis 2015 South University2 Performing Re ✓ Solved

Performing Regression Analysis using a linear regression model involves several steps. First, click on the “Statistics” tab, then select “Simple Regression.” Choose the appropriate “response variable” and “predictor variable.” Next, under the “Graphs” tab for Simple Regression, you may select to plot the “Residual Plots” and click OK.

The results of the regression and least squares line can be summarized by the following equation: Early Births per 100,000 = 105.0 – 4.322 Doctors per 100,000. In this equation, the intercept is 105.0 and the coefficient in front of X is 4.322. This formula can be used for analyses to predict the number of early births based on the number of doctors per capita.

Dot plots provide a visual representation of the relationship between two variables. To create dot plots in Minitab, manually enter the data first. Next, select the data entered and click on the “Graphs” tab. Choose “Scatterplot” and then select the “Simple” scatterplot under the single Y Variable category since there is one x and one y variable to plot. After selecting the appropriate variable for each variable type, click OK.

After generating the scatterplot, you may measure the strength of the correlation between the two variables. Highlight the data, click on “Statistics,” then select “Correlation,” and enter the two variables to test for correlation. Click OK to view the results.

The Pearson correlation for the selected data was found to be 0.791, with a p-value of 0.006. This indicates a strong linear correlation that is statistically significant, given that the p-value is less than 0.05.

Paper For Above Instructions

Regression analysis is an essential statistical tool used to understand relationships between variables. In this paper, we will delve into the steps for performing simple regression analysis using Minitab, interpreting the results, and discussing how dot plots can aid in visualizing these relationships. A specific example will illustrate how early births in a population relate to the number of doctors per 100,000, while also discussing the significance of Pearson's correlation coefficient.

Understanding Simple Regression

Simple regression analysis aims to examine the linear relationship between one dependent variable and one independent variable. In our case, the dependent variable is early births per 100,000, and the independent variable is the number of doctors per 100,000. This analysis helps predict outcomes based on the changes in predictor variables.

Procedure for Performing Regression Analysis

To perform regression analysis in Minitab, follow these steps:

  • Open Minitab and select the “Statistics” tab.

  • Click on “Simple Regression.”

  • Select the response variable (early births) and the predictor variable (doctors).

  • To analyze the residuals, navigate to the “Graphs” tab within the Simple Regression options and select “Residual Plots.”

  • Click OK to run the analysis.

Interpreting the Regression Results

The output of the regression analysis will provide an equation in the form:

Early Births per 100,000 = 105.0 – 4.322 Doctors per 100,000

Here, 105.0 represents the intercept, which is the expected number of early births when the number of doctors is zero. The coefficient of -4.322 indicates that for every additional doctor per 100,000, the early births drop by approximately 4.322 occurrences. This negative relationship suggests that an increase in the number of practitioners is associated with a reduction in early birth rates.

Visualizing Relationships with Dot Plots

Dot plots are a great visual tool for displaying relationships between two quantitative variables. By entering the data in Minitab and creating a scatterplot, we can visually assess how the two variables interact.

To create a dot plot, perform the following steps:

  • Manually enter the data into Minitab.

  • Highlight the data and navigate to the “Graphs” tab.

  • Select “Scatterplot” and choose “Simple” scatterplot.

  • Select the appropriate x and y variables and click OK.

The scatterplot generated will visually demonstrate the data points corresponding to early births and doctors per 100,000, highlighting any trends present in the data.

Assessing Correlation

After visualizing the relationship, it’s critical to quantify it. Correlation analysis measures the strength and direction of the linear relationship between two variables. In Minitab, you perform this measure by selecting “Statistics” and then “Correlation.” Enter the two variables you want to analyze, and the program will output a Pearson correlation coefficient along with a p-value.

For our analysis, we found a Pearson correlation coefficient of 0.791 with a p-value of 0.006. This high correlation indicates a strong relationship between the number of doctors and the rate of early births, and the p-value confirms that this relationship is statistically significant.

Conclusion

In conclusion, performing regression analysis and correlational statistics can provide profound insights into the relationships between variables. The negative relationship identified between the number of doctors and the incidence of early births offers vital information for public health policy and resource allocation. As demonstrated, Minitab serves as a robust tool for conducting these analyses, providing both visual and quantitative outputs that enhance our understanding of the data.

References

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