The Scatter Chart for a Linear Regression_default

Introduction to Simple Linear Regression in Excel

Purpose: This guide demonstrates how to run a basic simple linear regression analysis using Excel's Data Analysis Toolpack, with a focus on evaluating the relationship between the number of Starbucks stores in each state and the population of those states.

Data Focus: The analysis will highlight the correlation between the dependent variable (number of Starbucks stores) and the independent variable (population), which may serve as a useful model for understanding business distribution based on demographics.

Steps to Execute Regression

Step 1: Access Data Analysis Tool

1. Open Microsoft Excel and navigate to the Data tab on the ribbon.

2. In the Analysis group, click on Data Analysis to open the Data Analysis dialog box, which comprises various statistical tools.

Step 2: Choose Regression

1. From the drop-down list in the Data Analysis dialog, select Regression and click OK. This action will lead you to a new configuration window specifically for regression analysis.

Step 3: Define Input Ranges

1. In the Regression dialog box, define your ranges:

   • Y Range: Select the range that includes the number of Starbucks stores (the dependent variable).

   • X Range: Select the range that encompasses the population figures (the independent variable).

2. Ensure that the specified ranges for Y and X contain the same number of data points to maintain consistency.

3. If labels are included in the top row of your selected ranges, remember to check the appropriate box.

Step 4: Set Output Range

1. Choose where you would like the regression output to be displayed by clicking on the desired cell in the worksheet. It's advisable to choose a location that does not overlap with your existing data.

Step 5: Configure Outputs

1. To enhance your analysis, check the box for Residuals to assess how far estimated values deviate from the actual data points.

2. Also, select Line Fit Plot for graphical visualization of the residuals on a chart.

3. Once configurations are complete, click OK to generate the regression analysis output automatically.

Understanding Regression Output

The output will include two primary components: a regression statistics table and graphical representation.

Scatter Chart:

1. The scatter chart displays actual data points in blue, representing the observed number of Starbucks stores against the fitted values derived from your regression model.

2. The orange squares represent predictions made by the regression model.

3. If required, these predictions can be removed by selecting the orange points and deleting them, allowing for a clearer visual of the actual data points.

Adding Trend Line and Regression Equation

Visualizing the Actual Data:

1. To enhance interpretability, click on any blue data point in the chart, right-click to access options, and select Add Trendline.

2. Choose Linear as the trendline option to reflect a straightforward linear relationship.

3. Check the boxes to display both the Equation on chart and the R-squared value, which indicates how well the regression line fits the data.

Conclusion

Benefits of this Method:

• The inclusion of a trendline and regression equation directly correlates with regression analysis calculations performed in Excel, providing an accurate representation of the relationship modeled.

• Utilizing this method avoids potential errors associated with misidentifying X and Y values when using separate scatter sheets.

• This streamlined process significantly aids in visualizing and interpreting the relationship between population and the number of Starbucks stores, which can be invaluable for strategic business planning and market analysis.