Regression Analysis and Data Plotting in Excel

Overview of Regression Analysis

• Regression analysis is a statistical method to analyze the relationship between two variables.
• The focus of the example is on UV absorbance and sunscreen concentration but is illustrated using helium volume and temperature data.

Data Context

• The experiment involves examining how the volume of helium varies with temperature.
• Temperature is measured in Kelvin, and volume is measured in liters.
• The objective is to determine the volume of helium at 25 degrees Celsius by analyzing this relationship.

Steps for Data Analysis using Excel

1. Open Excel: Begin by launching a new Excel spreadsheet.

2. Input Data: Enter the provided data set into the spreadsheet, ensuring:

   • Temperature values are in one column (e.g., Column A).
   • Volume values are in another column (e.g., Column B).

3. Plotting Data:

   • Highlight the data.
   • Choose a scatter plot (select the first option for a simple scatter).
   • Ensure that temperature is set to the x-axis and volume to the y-axis.

4. Labeling Axes:

   • Click the green plus sign next to the graph to add axis titles and labels:
     • X-axis: Temperature (in Kelvin)
     • Y-axis: Volume of Helium (in liters)

5. Adding a Trend Line:

   • Right-click on the data points in the scatter plot.
   • Select “Add Trendline” to visualize the relationship between temperature and volume.
   • Display the R-squared value on the chart to assess the fit of the trendline.

Understanding R-squared Value

• R-squared indicates how well the trend line approximates the data points.
  • A value of 1 indicates all points lie on the line.
  • Values above 0.98 are preferred for a strong correlation.

Forecasting and Extrapolation

• Discusses the difference between interpolation and extrapolation:
  • Interpolation: Predicting values within the range of data points.
  • Extrapolation: Predicting values outside the range of data points using the trendline.
• In this case, we forecast backward to find data for 150 Kelvin.

Final Calculation

1. Conversion:

   • Convert 25 degrees Celsius to Kelvin:
     • 25 + 273 = 298 Kelvin.

2. Using the Equation of the Line:

   • Substitute x = 298 into the regression equation.
   • Example equation form: y = mx + b
     • Where m is the slope and b is the y-intercept.
   • Substituting values, solve for volume:
     • Given: y = 0.1078(298) - 8.0933
   • Calculate to find volume:
     • Final result: Volume of helium = 24 liters.

3. Verification:

   • Check the result on the graph by following the line to see if the expected volume aligns with 24 liters.

Conclusion

• Emphasized the importance of checking calculations visually against the graph.
• Next step: apply learned methods in the lab for practical experimentation.