问一道题：NO.PZ2018101001000031

问题如下：

Paul does the regression analysis of X and Y and gets the following results:

What is 90% confidence interval for the coefficient on X if n is 102？

选项：

[1.4290,10.8024]

[2.2624,10.8024]

[2.2624,11.6358]

解释：

B is correct.

考点: Regression Coefficient Confidence Interval.

解析: Regression Coefficient Confidence Interval的公式是$\widehat{b_1}\pm t_c{S}_{\widehat{b_1}}$ ，这里的$\widehat{b_1}$等于6.5324， $S_{\widehat{b_1}}$等于2.5723。已知n为102，所以自由度$（$df$）$等于100。查T分布表可得，当$\alpha$为10%，df=100时的分界点为1.660，即$t_c=1.660$ 。所以X的系数的置信区间为6.5324±1.660×2.5723，即[2.2624,10.8024]