Sanity check on regressions
Hi - just need some input on this one. Simple practice q from Kaplan:
Coefficient Standard Error
Intercept 2.1 2.01
Index 1.9 0.31
Q: If the return on the industry index is 4%, the stock’s expected return would be
A: 9.7% (C) because
Y = b0 + b1X
Y = 2.1 + 1.9(4) = 9.7%
I get that if you follow the formula (Y = mX + b) and plug and chug, you’ll get that answer. My confusion comes from the following: what does that coefficient of 1.9 represent? It is the slope of the regression (aka this stock’s beta). It represents a 1.9% expected change in the stock for any 1% change in the index.
Therefore if the index changes 4%, why isn’t our expected change simply 4 x 1.9 = 7.6% ? Why does the y-intercept (the value if our index changed by 0%, which we know if didn’t) required in this calculation? Do you get what I’m saying from a step back and away from the simple formula? Thanks
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