1SUMMARY OUTPUT Regression Statistics 4 Multiple R 5 R Square 6 Adjusted R Squar

Question

1SUMMARY OUTPUT Regression Statistics 4 Multiple R 5 R Square 6 Adjusted R Square 7 Standard Error 8 Observations 0.638460684 0.407632045 0.407263543 1487710.983 3218 10 ANOVA df MS 4.8966E+15 2.4483E+15 1106.184945 SignificanceF 0 12 Regression 13 Residual 14 Total 3215 7.11571E+15 2.21328E+12 3217 1.20123E+16 Coefficients Standard Error t Stat 96341.99665 28196.73159 3.416778869 0.000641535 41056.60486 10.25948913 0.236961279 43.29605733 1.085354691 0.114119612 -9.510676352 3.58645E-21 -1.309109256 P-value Lower 95% 17 Intercept 18 BLDGS 19 LAND 20 21 0 9.794878644 Sheet2 Sheet1 + 100% al

Explanation / Answer

SOLUTION:

   In multiple linear regression, we try to estimate the value of one dependent variable by using the values of two or more independent variables. In order to get an estimate of the dependent variable, provided we have the values of the independent variables, we try to fit a multiple linear regression model.

   However, it may so happen that the estimated value might not be always 100% accurate. This means that some variation can be assigned to the independent variables but there still exists some error (or unexplained) variation. In order to see how accurate the fitted model is, we compute coefficient of determination (R2) which gives a measure of how much variation is explained by the independent variables.

   So here, we have the value of R2 as 0.407632045 i.e. 40.76% and the two independent variables are BLDGS and LAND. So this value of R2 implies that 40.76% of variation is explained by the independent variables. In layman's terms, it means that using this model, if we try to estimate the value of the dependent variable, there is a 40.76% chance that the estimated value is almost fully accurate.

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