自由度为啥是n-2

问题如下：

Paul Peter is analyzing the performance of the stock ABC over the past 4 years.

Peter estimates a linear regression using excess monthly returns on Stock ABC as the dependent variable and excess monthly returns on the S&P 500 index (exS&P) as the independent variable. The data are expressed in decimal terms (e.g., 0.05, not 5%).

exABC_t = b₀ + b₁ (exS&P_t) +ε_t

Results from that analysis are presented in the following figures.

3. Peter would like to test the following hypothesis: H₀: B₁ ≤ 1 vs. HA: B₁> 1 at the 5 % significance level. The calculated t-statistic and the appropriate conclusion are:

Give the t-critical values as follow:

the t-critical values are all two-tails

选项：

A. B. C. D.

解释：

B is correct.

考点：Hypothesis Test in Linear Regression

解析：因为是48个月的数据，所以n=48。本题应该去查单尾95%的df=48-2=46的数据，即双尾90%的df=46的数据。 the critical one-tailed 95% t-value = the critical two-tailed 90% t-value= 1.679

斜率项的t检验值=(1.5863-1)/0.0744=7.88>1.679。所以应该拒绝原假设。