# Multiple Regression Analysis

**Introduction**

The paper discussion focuses on multiple regression analysis. The study involves the company’s vice president who wants to know how regression analysis can be used in predicting bond rates. Therefore, the Jon conducted analysis using the predictor variables, dummy, and dependent variables to conduct the analysis. The dummy variables were the coded bond ratings. The dependent variables included interest rate, utility ratio, the U.S. Treasury bond rates, bond maturity and prime lending rate. The analysis focuses on establishing the relationships between the interest rate paid during the time bond was used and the U.S. Treasury bond rate. Also, the analysis objective is to determine the relationship between the dependent variable and the prime lending rate. Thus, the analysis is to determine which variables that have a positive and negative relationship.

The multiple regression analysis is important on predicting the variable values based on two or more values. Thus the analysis will assist the company in establishing how the different variables involved in bond issuance relate. The company wants to calculate the economic statistical coefficients that will help in showing how strong is the relationship between different variables involved.

**Hypothesis statement**

The purpose of the analysis is to test how do interest rate paid by the utility during the time bond was used and the U.S. Treasury bond rate. Also, the analysis objective is to determine the relationship between the dependent variable and the prime lending rate. Also, the multiple regression analysis wants to capture, by what degree or percentage a change in one variable cause other variables to change. Thus the regress analysis wants to test this hypothesis.

**Data presentation and interpretation**

The Jon report indicated the following:

1. The regression equation is Interest (I) = -1.28-.929AA-1.18AA+1.23 Bonds rates +0.0615 maturity.

The R squared shows how many points fall in the best line of fit. Therefore, almost 1% of the line falls in the best line of fit. The Adjusted R squared shows how does the interest rate paid by utility adjust to changes in the U.S. Treasury bond rate. The observation in the model shows the number of elements in the data.

#### Coefficient

Also, the R squared show the variation of independent variables to the dependent variable. Thus there is a positive relationship between the independent and dependent variable. Also, the predictor variable also has a positive relationship. Hence since the P value is large than common Alfa value of 0.05, the model is statistically insignificant. Therefore interest rate paid by the utility during the time bond was used, and the U.S. Treasury bond rate P values are not statistical important at 95 percent (95%) confidence level.

#### 1. 1.28-.929AA-1.18AA+1.23 Bonds rates +0.0615 Maturity

From the equation the line of best-fit intercept y-axis at point 1.23. The coefficient of the interest rate is 0.929.Thus, an increase in interest rates by paid utility increase the U.S. Treasury bond rate by 92.9%. The interest rate paid by utility has negative coefficient signifying that the interest rates influence the bond rate. The p-values and t-values in regression model demonstrate that the ratio of earnings to fixed charges has no significant impact on predicting the interest rate paid by utility taking into account the time of issuance. Therefore, the company should use the regression model to predict bond rates. The regression analysis proves that the is relationship between different variables in the case.