Investment analysts generally believe the interest rate on b

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. 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 values from the chart (right click on the data points, select Add Trend line, and select options to show these metrics).

Do you think the bond rate can be predicted by the prime interest rate? Justify your answer using the relevant metrics.

Bond Rate Prime Interest Rate

5% 16%

12 6

9 8

15 4

7 7

Solution

Using technology, we get              
              
slope =    -0.714622642          
intercept =    15.45990566          
              
Thus, the regression line is              
              
y^ =    -0.714622642   x   +   15.45990566 [ANSWER]

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Also, getting the correlation,              
              
r =    -0.827782344          
              
Thus, the coefficient of determination is              
              
r^2 =    0.685223609  

Thus, looking at r and r^2, it looks like that the bond rate can really be predicted by the prime interest rate, as they r^2 value is quite high. Around 68.5% of the variation in bond rate is explained by prime interest rate.

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