In a Study of the Bidding Behavior When Antique Grandfather

question 46

Essay

In a study of the bidding behavior when antique grandfather clocks are sold at auction, investigators analyzed the selling price (y) and the age in years of the grandfather clock (x). Summary quantities from this analysis yield: n = 32 S_xx = 23625.9 s_e = 273.03 ​
a) Calculate the estimated standard deviation of a + bx* for x* = 150.
b) For what value x* is the estimated standard deviation of a + bx* smallest, and why?

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Definitions:

Firm's Beta

A measure of a stock's volatility in relation to the overall market; a beta greater than 1 means the stock is more volatile than the market, while a beta less than 1 means it is less volatile.

Single-Factor Market Model

A financial model that explains a security's returns as the outcome of a single market-wide factor and the security's sensitivity to that factor.

Unsystematic Risk

The risk associated with a specific company or industry that can be mitigated through diversification.

Residuals

Residuals are differences between observed and predicted values in statistical models, used to assess the fit of models to data.