Testing a coefficient We’ll use the data and printouts Antelope are beautiful and graceful animals...

Testing a coefficient

We’ll use the data and printouts Antelope are beautiful and graceful animals that live on the high plains of the western United States. Thunder Basin National Grasslands in Wyoming is home to hundreds of antelope. The Bureau of Land Management (BLM) has been studying the Thunder Basin antelope population for the past 8 years. and test the significance of x₃ as an explanatory variable using level of significance a = 0.05.

H₀: β₃= 0 and H₁: b₃≠ 0

To find the t value corresponding to b₃, we use Equation (16) and the null hypothesis H₀: b₃= 0 . This gives us the equation

(16)

(17)

 

In the regression analysis shown in Figure 9-21, we see a t value for the constant and each coefficient. This t value is exactly the value of t = b_i/S_i. This is the t value corresponding to the sample test statistic. For the coefficient of x₃, we see

t value ≈ 3.65

FIGURE 9-21 Minitab Display of Regression Analysis