# Essays on The Linear Regression Model Assignment

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The paper 'The Linear Regression Model' is a perfect example of a finance an accounting assignment. In a regression model, there are two kinds of variable – response variable and explanatory variable. Response variables are the "outputs" of a regression model. Explanatory variables, on the other hand, are the "inputs" of the regression model. Response variables are dependent on the explanatory variables. Explanatory variables are independent of the response variables. The linear regression model assumes that there is a linear, or "straight line, " relationship between the dependent variable and each predictor. This relationship is described in the following formula. Subsequently, regression analysis was conducted using only significant predictors.

The model was found to be significant. That is, the variation explained by the model is not due to chance. The adjusted R-Sq value shows the model (Score, Experience, and Market) predicts about 48 percent of the variation in Bonus. Model two is better because none of the predictors in model two was found insignificant. R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points.

An R2 of 1.0 indicates that the regression line perfectly fits the data. Adjusted R2 is a modification of R2 that adjusts for the number of explanatory terms in a model. Unlike R2, the adjusted R2 increases only if the new term improves the model more than would be expected by chance. The adjusted R2 can be negative, and will always be less than or equal to R2.The semi-automatic procedure BREG is a method used to help determine which predictor (independent) variables should be included in a multiple regression model.   This method involves examining all of the models created from all possible combination of predictor variables.

Best Subsets Regression uses R2 to check for the best model.   It would not be fun or fast to compute this method without the use of a statistical software program.   First, all models that have only one predictor variable included are checked and the two models with the highest R2 are selected.   Then all models that have only two predictor variables included are checked and the two models with the highest R2 are chosen, again.   This process continues until all combinations of all predictors variables have been taken into account.

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