Answers
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.
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