Question

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 least squares regression line to predict bond rates by the prime interest rate.

Bond Rate	Prime Interest Rate
5%	13%
11	6
9	8
15	4
7	7

Answer 1

Here we have R codes:

CODE:

bond <- c(5,11,9,15,7)
prime <- c(13,6,8,4,7)
cor(bond,prime)
summary(lm(bond~prime))

OUTPUT:

> bond <- c(5,11,9,15,7)

> prime <- c(13,6,8,4,7)

> cor(bond,prime)

[1] -0.8737926

> summary(lm(bond~prime))

Call:

lm(formula = bond ~ prime)

Residuals:

1 2 3 4 5

1.000e+00 1.110e-16 4.996e-16 2.000e+00 -3.000e+00

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 17.0000 2.6262 6.473 0.00748 **

prime -1.0000 0.3213 -3.112 0.05279 .

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.16 on 3 degrees of freedom

Multiple R-squared: 0.7635, Adjusted R-squared: 0.6847

F-statistic: 9.686 on 1 and 3 DF, p-value: 0.05279

Here we can see the correlation between them is -0.8737926, so there is a good linear relationship between them. So we predict the bond rate be predicted by the prime interest rate.

Here is the equation,

Bond rate = 17 - 1 * Prime interest rate.