### Example : Estimating Beta for Westport Innovations Stock

Westport Innovations Inc. (Westport) is a Canadian company that provides low-emission engine and fuel system technologies utilizing gaseous fuels. Its stock trades on the Toronto Stock Exchange (Ticker: WPT).

You are an investor in Westport's stock and want an estimate of its beta. You hypothesize that Westport has an average level of market risk and that its required return in excess of the risk-free rate is the same as the market’s required excess return.

One regression that summarizes these statements is

(R − RF ) = α + β(RM − RF ) + ε

where,

RF is the periodic risk-free rate of return (known at the beginning of the period)

RM is the periodic return on the market

R is the periodic return to the stock of the company

B measures the sensitivity of the required excess return to the excess return to market

Estimating this equation with linear regression provides an estimate of β , β^, which tells us the size of the required return premium for the security, given expectations about market returns.

Our calculator shows data from December 2008 through December 2013 (n = 61) of Westport stock prices , a risk-free interest rate, and the values of the market index. The return to Westport Stock is (R). The monthly return to 1 month Treasury bills is RF. The return to the S&P 500/TSX Composite Index is RM.

To see whether Westport stock has the same required return premium as the market as a whole, determine whether the null hypothesis (H_{0}: β = 1) is rejected in favor of alternative hypothesis (H_{a} : B ≠ 1 ) or not rejected at the 0.05 level of significance.

Additionally, how much of Westport stock's excess return variation can be attributed to company-specific risk?

**Testing Slope in regression**