Source | SS df MS Number of obs = 950 -------------+----------------------------
ID: 3310591 • Letter: S
Question
Source | SS df MS Number of obs = 950
-------------+---------------------------------- F(2, 947) = 172.50
Model | 2.6336e+11 2 1.3168e+11 Prob > F = 0.0000
Residual | 7.2289e+11 947 763350544 R-squared = 0.2670
-------------+---------------------------------- Adj R-squared = 0.2655
Total | 9.8625e+11 949 1.0393e+09 Root MSE = 27629
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SHW | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
NFM | 778.9416 374.1405 2.08 0.038 44.70131 1513.182
THISQ | 4.84e-08 2.65e-09 18.29 0.000 4.32e-08 5.36e-08
_cons | 18032.74 1996.962 9.03 0.000 14113.76 21951.73
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Interpet the results of the above data
Explanation / Answer
The test statistic MS(model)/MS(residual) is following F(2,947) distribution(this is a property of these type of tables).From here,we can tell that there are 2 independent predictor variables in the model.And,the error degrees of freedom is=947.So,total degrees of freedom=947+2=949.So the sample size is 1000.Now,p-value of the F statistics is 0.0000<<<0.05,which means the model is significant.But,there is a massive problem in this analysis.R-sq value is as low as 0.2655,which means that R^2 is able to explain only 26.55% of the total variation present in data.So,it will not give correct prediction for future observations,since the future observations will not be properly explained by he model.For this reason,the confidence interval that has been found,can not be used for future decisive purposes.The regresseion line fitted here is linear.For linear regression we assume that homoscedasticity and autocorrelation is absent and the error terms identically and independently follow normal distribution. May be,one or more of these assumptions are not valid for the data.May be,the errors are not normally distributed.Hence,the confidence interval that has found can not be used for future.We have to model the the data correctly for analysis purpose.From table only,we can see that model SS is only 1/3 of the residuall SS,but for correct models,model SS should be more than the residual SS. So,even if we interprete the variables,it has no meaning as the model is not correct. coef values of a variable is actually change in response per unit increase in value of the corresponding variable.
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