Please see restaurant stocks below coefficients. I ran a 3 factor fame french re

Question

Please see restaurant stocks below coefficients. I ran a 3 factor fame french regression below for these. can you please explain the differences in the coefficients or what they have in common?

Coefficients WEN BKW MCD CMG PZZA DPZ PZA.TO RRGB DRI Adjusted R Square 0.91761216 0.925583017 0.971617387 0.931762 0.965368 0.919818 0.884083 0.985714 0.849411 Intercept -0.002545964 -0.001019193 -0.001068157 -0.00291 -0.00076 -0.00043 0.001641 -0.00084 0.001641 mktrf 1.229208265 0.92143067 0.965888752 1.021481 0.992665 0.985481 0.859572 0.996073 0.859572 smb 0.259122397 -0.083744401 -0.111553407 -0.00768 -0.11464 -0.01648 -0.07738 -0.02058 -0.07738 hml 0.120594264 -0.200901985 0.029500481 -0.0168 -0.10562 -0.04741 -0.02779 0.042345 -0.02779

Explanation / Answer

Firstly, the data should be supported by the p-values and the t statistic which will tell about the significance of the variables and hence, how relevant they are. But given that we need to follow Fama French 3 variable model itself, that won't be very relevant.

Now coming to the data, I'll try to analyze the data from variable to variable across all the stocks.

1. Adjusted R Squared - This tells us about how well the model explains the variability in the actual stock and usually a value above 0.90 is considered good which means 90% of the variability in the stock movement can be explained by the Fama French Model. In this data, only PZA.TO and DRI have values less than 0.9 and thus, the model is comparatively less fitting into their data.

2. Intercept - A negative value here denotes a value of negative for the stock when the 3 independent variables in the model are zero. The coefficient in the model denotes the risk free rate and alpha.

3. mktrf - Here, a coefficient greater than 1 denotes that the stock price increases more than the increase in the variable.

4. smb - Negative value of this variable (Small minus Big market capitization) denotes that the value decreases with the increase in this variable.

Thus, this is how we can interpret the values and this tells us how the model fits into the stock prices and also, how the variables affect the stock price thus the relationship between the price and these variables for the stocks.

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