Statistics 401 Mod 5 Case - Multiple Regression Analysis - Coursework Example

In the normal regression analysis, we usually use regression to establish the relationship between a variable and another variable. In such a case, it is establish whether or not the changes in one of the variables affect the other variable. The one which is affected is the dependent variable because it depends on the changes of the other so as to have its changed value. The one which is being depended upon to change is the independent variable because it changes on its own. This is for instance in the case where harvest from a corn field is being tested to establish whether or not it has a relationship with the amount of rainfall in the year.

The harvest is the dependent variable while the rainfall amount is the independent variable. In the case of multiple regression analysis, the independent variables are more than one. . In this analysis where in this case assignment we were looking at housing starts again, this time we added another variable to the equation.  The historical values above give interest rates, lumber prices (dollars per board-foot) and number of starts.  We computed a multiple regression equation using these variables, with starts as the DV.

  Interest and price are the IVs.   From the computation of the regression analysis, I obtained the results shown above using the excel multiple regression. The regression analysis involved using the Housing stats as the Y variables in the excel regression file, and both the interest rate and the Price per board foot as the X variables. Based on the results of the regression as shown in the excel except above, the regression formula that I computed is of the form Y = a1*X1 + a2*X2 + b Where Y = number of housing starts X1 = interest rates a1 = regression coefficient of interest rates X2 = lumber prices a2 = regression coefficient of lumber prices b = constant.

The values of a1 and a2 correspond to the values on the Regression coefficients table shown above. The value of a1 is that on the interest rates coefficients which is -1203318. Likewise, the value of a2 is that on the price per board foot coefficient which is -17836.8. The value of the constant b is also found on the coefficients table. It is the value of the sample estimate of the standard deviation of the error In this case it has the value 155138.1. X1 and X2 are of course variables that correspond to the interest rates and the price per board foot respectively.

In turn, the formula thus becomes:- Y = -1203318*X1 + -17836.8*X2 + 155138.1 Using this formula, it is now much easy to do