Question

Examine the following summary output from Excel to answer questions that follow. SUMMARY OUTPUT R Square Adjusted R Square Standard Emor 0 9397848 0.8831955 0 8520477 34997867 20 ANOVA MS 1389.222401 347 3056 28.35493 0.00007729 83 7275992 12.248507 Reidual Total 15 19 157295 Coeicients Standard tmor tSta 88 53136 04969034 0.0018124 -00161801 11.51700364 76869966 14-06 0.272030159 1.626648 0047719 0.001405434 12895335 00216742 0011211971 1441326 0.0170043 1945621-06 08455571 00311086 a. Write the regression model (equation) that incorporates all the variables b Should one include all the independent variables in the model? In other words is this model a good prediction equation? Justify Suppose that the model with only x1 and x2 has R-squared value of 0.79 Has the addition of the other variables improved euracy of the regression model? Be specific. Why?

Answer 1

a. The regression model is as follows

y=-0.4969004(X1) + 0.0018124(X2) - 0.0161601(X3) + 0.00000164(X4) + 88.531168

b. The R squared value i.e. the coefficient of Determination is 0.8832 indicating 88.32% of the variation of y-values around the mean are explained by the x-values. The more near to 100 %, the better is the equation. Thus in this case, the model is a good prediction equation.

c. Here we look for adjusted R-squared value. Notice that 4 independent variables mean 4 predictors. They have adjusted R squared value as 0.852. Now, if we consider only first two variables, then the predictor is 2. In this case, the adjusted R-squared is 0.79. So there is a reduction in adjusted R-squared with reduction in predictors. Thus, addition of two variables actually increase the accuracy.

Incase had the addition of variables lowered the adjusted R-squared, then we could have said that the original equation is more accurate.