What is the estimation of standard deviation of errors and the explained variati

Question

What is the estimation of standard deviation of errors and the explained variation?

A real estate agency is modeling sale price of a house. The analyst collects following set of variables in order to set up her model: Sales price (y) of a house (in thousand dollars), size (x1) (in square feet), number of rooms (X2), number of bedrooms (x3) and age of the house (%). Questions 1-8 use following information The following regression output is obtained. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.907876319 0.82423941 0.796117716 26.42280179 30 ANOVA MS Significance F df 4 81852.06063 20463.01516 29.30973501 4.11825E-09 Regression Residual Total 25 17454.11137 698.1644546 29 99306.172 t Stat P-value Lower 95% Upper 95% Intercept Size Rooms Bedrooms Age Coefficients Standard Error 22.39576661 21.96161101 1.019768841 0.317605789 -22.83501795 67.6265511 0.088716834 0.021359476 4.153511646 0.000333729 0.044726169 0.13270749 23.62472664 5.791040725 4.079530392 0.4156264 11.69785501 35.5515982 40.16276527 12.30837287 -3.263044245 0.3182643 -65.51233372 -14.8131968 1.014151547 0.236837018 4.28206518 0.000239449 -1.501926516 -0.5263765

Explanation / Answer

from above:estimation of standard deviation of errors =(MSE)1/2 =(698.1644546)1/2 =26.4228

explained variation =(SSR/SST) =81852.06063/99306.172=0.824239

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