Question

Can you give me a simple interpretation of this output?

Call:

lm(formula = NOCRF ~ Mktrf + HML + SMB + SMB2)

Residuals:

     Min       1Q   Median       3Q      Max

-10.1560 -0.6880 -0.0254 0.6660 21.9700

Coefficients:

            Estimate Std. Error t value Pr(>|t|)   

(Intercept) -0.01163    0.02800 -0.415    0.678   

Mktrf        1.25614    0.02389 53.540 <2e-16 ***

HML          2.01719    0.04238 47.602   <2e-16 ***

SMB         -0.05150    0.04769 -1.080    0.280   

SMB2         0.03180    0.03545   0.897    0.372

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.585 on 3848 degrees of freedom

Multiple R-squared: 0.6676, Adjusted R-squared: 0.6672

F-statistic: 1882 on 4 and 3748 DF, p-value: < 2.2e-16

Answer 1

The p-value of Mktrf and HML are less than 0.05 while the p-value of SMB and SMB2 are greater than 0.05.

So on the basis of p-value, we have only two significant variables whose parameters (coefficient) in the equation are not zero while SMB and SMB2 are insignificant variables because their coefficient does not affect the response variable NOCRF, hence their affect are almost zero. So in this equation of multiple linear regression model we have only significant variables that could be added in the equation.

The R squared is 0.6676 it shows that the model is a good fir but since it is not 1 or close to 1, so we have chance to add more variables so that R squared can be increased upto 1. If it is 1, model is best fit.