The F-statistic
The F-test determines whether all the independent variables help explain the dependent variable. It is a test of regression’s overall significance that involves testing the null hypothesis that all the slope coefficients in the regression are jointly equal to zero…
Assumptions of Multiple Regression Model
Multiple regression models are built on the following assumptions. The relationship between the dependent variable, \(Y\), and the independent variables, \(X_{1}, X_{2},…, X_{k}\) is linear. The independent variables \((X_{1}, X_{2},…, X_{k})\) are not random. There exists no definite linear relationship between…
The Predicted Value of a Dependent Variable
The Predicted Value of the Dependent Variable The following steps are followed to predict the value of a dependent variable in a multiple regression model. Determine the regression coefficient estimates. Obtain the forecasted values of the independent variables. Calculate the…
Interpreting the Results of Hypothesis Tests of Regression Coefficients
The following results are obtained from regressing the price of the US Dollar Index (USDX) on inflation rates and real interest rates. $$\small{\begin{array}{l|c}\textbf{Regression Statistics}\\ \hline\text{Multiple R} & 0.8264\\ \hline\text{R Square} & 0.6830\\ \hline\text{Adjusted R Square} & 0.5924\\ \hline\text{Standard Error} &…
Estimated Regression Coefficients
The intercept term is defined as the value of the dependent variable when the independent variables are zero. On the other hand, each slope coefficient is the estimated change in the value of the dependent variable for a one-unit change…
Multiple Regression Equation
Multiple regression allows us to evaluate the effect of two or more independent variables on a given dependent variable. Multiple regression with two explanatory variables and one intercept term can be represented in the following 3D diagram: Mathematically, a multiple…
Functional Forms for Simple Linear Regression
Most Financial and economic data exhibit non-linear relationships between the dependent and independent variables. Estimating such data using a simple linear regression model would lead to the dependent variable being understated for some ranges of the independent variable. Thus, we…
Prediction Using Simple Linear Regression
We calculate the predicted value of the dependent variable (Y) by inserting the estimated value of the independent variable (X) in the regression equation. The predicted value of the dependent variable (Y) is determined using the formula: $$\widehat{Y}=\widehat{b_{0}}+\widehat{b_{1}}X$$ Where: \(\widehat{Y}\)…
Hypothesis Testing
Hypothesis testing is used to test whether the estimated regression coefficients are statistically significant. Hypothesis testing can be performed using the confidence interval approach or the t-test approach. In the previous learning objective, we discussed the confidence interval approach. In…
ANOVA and Standard Error of Estimate in Simple Linear Regression
ANOVA is a statistical procedure used to partition the total variability of a variable into components that can be ascribed to different sources. It is used to determine the effectiveness of the independent variable(s) in explaining the variation of the…
