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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

  1. 11.2%
  2. 7.6%
  3. 9.7%

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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TeenageDiplomat wrote:
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’s return for any 1% change in the index’s return.

That’s better.

TeenageDiplomat wrote:
Therefore if the index’s return changes 4%, why isn’t our expected change of return simply 4% x 1.9 = 7.6% ?

It is.

TeenageDiplomat wrote:
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

So that we know the value of our stock’s return, not merely the change in its return.  When the index’s return changes by 4% from, say, 5% to 9%, does the return on our stock (which changes by 7.6%) change from 0% to 7.6%?  Or from 35% to 42.6%?  Or from −18.4% to −10.8%?

Simplify the complicated side; don't complify the simplicated side.

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