Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate for loans; that is bonds perform well when lending rates are down and perform poorly when interest rates are up. Can the bond rate be predicted by the prime interest rate?
Use the following data to construct a scatter graph and then fit a regression line to the data. Report the regression formula and the r-squared value from the chart (right click on the line, select "Add Trendline" and select options to show these metrics).
bond Rate/ Prime Interest Rate
5 % 16%
12 6
9 8
15 4
7 7
Regression formula: y = -2.8x + 14.2
R-squared value: 0.907
To construct a scatter graph and fit a regression line to the given data, follow these steps:
1. Arrange the data in two columns: one for the bond rates and the other for the corresponding prime interest rates.
Bond Rate (%) | Prime Interest Rate (%)
------------------------------------------
5 | 16
12 | 6
9 | 8
15 | 4
7 | 7
2. Open a spreadsheet program such as Microsoft Excel or Google Sheets.
3. Enter the bond rates in one column (e.g., column A) and the prime interest rates in another column (e.g., column B).
4. Select the data range in both columns (including the headers, so five rows in total).
5. Click on the "Insert" tab or menu, and then select "Scatter" from the chart options. Choose a scatter plot type that shows individual data points.
6. Once the scatter graph is created, right-click on any data point and select "Add Trendline".
7. In the trendline options, select the type of regression line you prefer (linear, polynomial, etc.).
8. Check the box to display the regression formula and the r-squared value on the chart.
9. Click "OK" to add the trendline.
The regression formula and the r-squared value will now be displayed on the scatter graph. The regression formula will show the mathematical relationship between the bond rate and prime interest rate, and the r-squared value will indicate how well the regression line fits the data points.
Note: The regression analysis assumes a linear relationship between the bond rate and the prime interest rate. If the relationship is non-linear, you may need to use different regression methods, such as polynomial regression.
To construct a scatter graph and fit a regression line to the data, follow these steps:
1. Create a table with two columns: "Bond Rate" and "Prime Interest Rate."
- Enter the given data in the respective columns:
Bond Rate (%) | Prime Interest Rate (%)
------------- | ----------------------
5 | 16
12 | 6
9 | 8
15 | 4
7 | 7
2. Once you have entered the data, select both columns of data by clicking and dragging over them.
3. Click on the "Insert" tab in your spreadsheet software (e.g., Microsoft Excel).
4. Locate the "Scatter" chart type and choose the one that plots points without connecting lines.
5. A scatter graph will be generated with the data points plotted.
6. Right-click on one of the data points on the graph and select "Add Trendline."
7. In the Trendline options, choose a linear regression model. Make sure to check the boxes to display the regression formula and r-squared value.
8. The regression formula will appear on the graph, and the r-squared value will be shown in the trendline options or near the formula.
Please note that if you provide the software you are using, I can guide you with more specific instructions.