{"id":1121857,"date":"2025-01-08T19:14:12","date_gmt":"2025-01-08T11:14:12","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1121857.html"},"modified":"2025-01-08T19:14:18","modified_gmt":"2025-01-08T11:14:18","slug":"%e5%a6%82%e4%bd%95%e5%be%97%e5%88%b0python-ols%e7%9a%84t%e5%80%bcp%e5%80%bc","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1121857.html","title":{"rendered":"\u5982\u4f55\u5f97\u5230python ols\u7684t\u503cp\u503c"},"content":{"rendered":"

\"\u5982\u4f55\u5f97\u5230python<\/p>\n

\u5982\u4f55\u5f97\u5230Python OLS\u7684t\u503cp\u503c<\/strong><\/p>\n<\/p>\n

\u5728\u4f7f\u7528Python\u8fdb\u884c\u7edf\u8ba1\u5206\u6790\u65f6\uff0c\u83b7\u53d6OLS\uff08\u666e\u901a\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09\u56de\u5f52\u6a21\u578b\u7684t\u503c\u548cp\u503c<\/strong>\u662f\u4e00\u4e2a\u91cd\u8981\u6b65\u9aa4\u3002\u4f7f\u7528statsmodels\u5e93\u3001\u638c\u63e1\u57fa\u672c\u7edf\u8ba1\u6982\u5ff5\u3001\u6b63\u786e\u89e3\u91ca\u7ed3\u679c<\/strong>\u662f\u5173\u952e\u6240\u5728\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528Python\u53ca\u5176\u76f8\u5173\u5e93\u6765\u83b7\u53d6OLS\u56de\u5f52\u6a21\u578b\u7684t\u503c\u548cp\u503c\uff0c\u5e76\u6df1\u5165\u89e3\u91ca\u8fd9\u4e9b\u7edf\u8ba1\u91cf\u7684\u610f\u4e49\u548c\u7528\u9014\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u51c6\u5907\u6570\u636e<\/h3>\n<\/p>\n

\u5728\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790\u4e4b\u524d\uff0c\u9996\u5148\u9700\u8981\u51c6\u5907\u597d\u6570\u636e\u3002\u901a\u5e38\uff0c\u6211\u4eec\u4f1a\u4f7f\u7528pandas\u5e93\u6765\u5904\u7406\u6570\u636e\uff0c\u56e0\u4e3a\u5b83\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u6570\u636e\u5904\u7406\u80fd\u529b\u3002\u6211\u4eec\u9700\u8981\u786e\u4fdd\u6570\u636e\u7684\u8d28\u91cf\uff0c\u5904\u7406\u7f3a\u5931\u503c\u3001\u5f02\u5e38\u503c\u7b49\u95ee\u9898\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff0c\u7528\u4e8e\u5c55\u793a\u5982\u4f55\u51c6\u5907\u6570\u636e\uff1a<\/p>\n<\/p>\n

import pandas as pd<\/p>\n
\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684DataFrame<\/strong><\/h2>\n
data = {<\/p>\n
    'X1': [1, 2, 3, 4, 5],<\/p>\n
    'X2': [2, 4, 6, 8, 10],<\/p>\n
    'Y': [1, 2, 1.3, 3.75, 2.25]<\/p>\n
}<\/p>\n
df = pd.DataFrame(data)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001\u4f7f\u7528statsmodels\u5e93\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790<\/h3>\n<\/p>\n
Statsmodels<\/strong>\u662fPython\u4e2d\u4e00\u4e2a\u5f3a\u5927\u7684\u7edf\u8ba1\u6a21\u578b\u5e93\uff0c\u5b83\u63d0\u4f9b\u4e86\u8bb8\u591a\u7edf\u8ba1\u6a21\u578b\u548c\u5de5\u5177\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5b83\u6765\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790\uff0c\u5e76\u83b7\u53d6t\u503c\u548cp\u503c\u3002<\/p>\n<\/p>\n
\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u5b89\u88c5statsmodels\u5e93\uff1a<\/p>\n<\/p>\n
pip install statsmodels<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790\uff1a<\/p>\n<\/p>\n
import statsmodels.api as sm<\/p>\n
\u5b9a\u4e49\u81ea\u53d8\u91cf\uff08X\uff09\u548c\u56e0\u53d8\u91cf\uff08Y\uff09<\/strong><\/h2>\n
X = df[['X1', 'X2']]<\/p>\n
Y = df['Y']<\/p>\n
\u6dfb\u52a0\u5e38\u6570\u9879<\/strong><\/h2>\n
X = sm.add_constant(X)<\/p>\n
\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790<\/strong><\/h2>\n
model = sm.OLS(Y, X).fit()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u83b7\u53d6t\u503c\u548cp\u503c<\/h3>\n<\/p>\n
OLS\u56de\u5f52\u5206\u6790\u5b8c\u6210\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7model\u5bf9\u8c61\u6765\u83b7\u53d6t\u503c\u548cp\u503c\u3002\u5177\u4f53\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
# \u83b7\u53d6t\u503c\u548cp\u503c<\/p>\n
t_values = model.tvalues<\/p>\n
p_values = model.pvalues<\/p>\n
print("T-values:")<\/p>\n
print(t_values)<\/p>\n
print("\\nP-values:")<\/p>\n
print(p_values)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001\u89e3\u91cat\u503c\u548cp\u503c<\/h3>\n<\/p>\n
t\u503c<\/strong>\u548cp\u503c<\/strong>\u662f\u56de\u5f52\u5206\u6790\u4e2d\u4e24\u4e2a\u91cd\u8981\u7684\u7edf\u8ba1\u91cf\u3002\u5b83\u4eec\u5206\u522b\u7528\u4e8e\u68c0\u9a8c\u6bcf\u4e2a\u56de\u5f52\u7cfb\u6570\u7684\u663e\u8457\u6027\u3002<\/p>\n<\/p>\n
1\u3001t\u503c<\/h4>\n<\/p>\n
t\u503c<\/strong>\u8868\u793a\u56de\u5f52\u7cfb\u6570\u9664\u4ee5\u5176\u6807\u51c6\u8bef\u5dee\u7684\u7ed3\u679c\u3002t\u503c\u8d8a\u5927\uff0c\u8bf4\u660e\u8be5\u7cfb\u6570\u663e\u8457\u4e0d\u4e3a\u96f6\uff0c\u5373\u8be5\u81ea\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u6709\u663e\u8457\u5f71\u54cd\u3002\u5e38\u89c1\u7684t\u503c\u9608\u503c\u4e3a1.96\uff08\u5bf9\u4e8e95%\u7684\u7f6e\u4fe1\u533a\u95f4\uff09\u3002<\/p>\n<\/p>\n
2\u3001p\u503c<\/h4>\n<\/p>\n
p\u503c<\/strong>\u8868\u793a\u5728\u5047\u8bbe\u56de\u5f52\u7cfb\u6570\u4e3a\u96f6\u7684\u524d\u63d0\u4e0b\uff0c\u89c2\u6d4b\u5230\u5f53\u524dt\u503c\u6216\u66f4\u6781\u7aef\u60c5\u51b5\u7684\u6982\u7387\u3002p\u503c\u8d8a\u5c0f\uff0c\u8bf4\u660e\u8be5\u7cfb\u6570\u663e\u8457\u4e0d\u4e3a\u96f6\uff0c\u5373\u8be5\u81ea\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u6709\u663e\u8457\u5f71\u54cd\u3002\u5e38\u89c1\u7684p\u503c\u9608\u503c\u4e3a0.05\uff08\u5bf9\u4e8e95%\u7684\u7f6e\u4fe1\u533a\u95f4\uff09\u3002<\/p>\n<\/p>\n
\u4e94\u3001\u6848\u4f8b\u5206\u6790<\/h3>\n<\/p>\n
\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u5982\u4f55\u5728\u5b9e\u9645\u4e2d\u5e94\u7528\u8fd9\u4e9b\u77e5\u8bc6\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4e00\u4e2a\u5b9e\u9645\u6848\u4f8b\u6765\u8fdb\u884c\u8be6\u7ec6\u5206\u6790\u3002<\/p>\n<\/p>\n
1\u3001\u52a0\u8f7d\u6570\u636e<\/h4>\n<\/p>\n
\u6211\u4eec\u5c06\u4f7f\u7528\u4e00\u4e2a\u516c\u5f00\u7684\u623f\u4ef7\u6570\u636e\u96c6\u8fdb\u884c\u5206\u6790\u3002\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u52a0\u8f7d\u6570\u636e\uff0c\u5e76\u8fdb\u884c\u521d\u6b65\u7684\u9884\u5904\u7406\u3002<\/p>\n<\/p>\n
import pandas as pd<\/p>\n
\u52a0\u8f7d\u6570\u636e\u96c6<\/strong><\/h2>\n
url = 'https:\/\/raw.githubusercontent.com\/selva86\/datasets\/master\/BostonHousing.csv'<\/p>\n
df = pd.read_csv(url)<\/p>\n
\u67e5\u770b\u6570\u636e\u96c6\u7684\u524d\u51e0\u884c<\/strong><\/h2>\n
print(df.head())<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5b9a\u4e49\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf<\/h4>\n<\/p>\n
\u5728\u8fd9\u4e2a\u6848\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u623f\u4ef7\uff08medv<\/code>\uff09\u4f5c\u4e3a\u56e0\u53d8\u91cf\uff0c\u5176\u4ed6\u53d8\u91cf\u4f5c\u4e3a\u81ea\u53d8\u91cf\u3002<\/p>\n<\/p>\n
# \u5b9a\u4e49\u81ea\u53d8\u91cf\uff08X\uff09\u548c\u56e0\u53d8\u91cf\uff08Y\uff09<\/p>\n
X = df.drop(columns=['medv'])<\/p>\n
Y = df['medv']<\/p>\n
\u6dfb\u52a0\u5e38\u6570\u9879<\/strong><\/h2>\n
X = sm.add_constant(X)<\/p>\n
<\/code><\/pre>\n<\/p>\n
3\u3001\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790<\/h4>\n<\/p>\n
# \u8fdb\u884cOLS\u56de\u5f52\u5206\u6790<\/p>\n
model = sm.OLS(Y, X).fit()<\/p>\n
<\/code><\/pre>\n<\/p>\n
4\u3001\u83b7\u53d6t\u503c\u548cp\u503c<\/h4>\n<\/p>\n
# \u83b7\u53d6t\u503c\u548cp\u503c<\/p>\n
t_values = model.tvalues<\/p>\n
p_values = model.pvalues<\/p>\n
print("T-values:")<\/p>\n
print(t_values)<\/p>\n
print("\\nP-values:")<\/p>\n
print(p_values)<\/p>\n
<\/code><\/pre>\n<\/p>\n
5\u3001\u89e3\u91ca\u7ed3\u679c<\/h4>\n<\/p>\n
\u901a\u8fc7\u67e5\u770bt\u503c\u548cp\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u5224\u65ad\u54ea\u4e9b\u81ea\u53d8\u91cf\u5bf9\u623f\u4ef7\u6709\u663e\u8457\u5f71\u54cd\u3002\u4f8b\u5982\uff0c\u5982\u679c\u67d0\u4e2a\u53d8\u91cf\u7684p\u503c\u5c0f\u4e8e0.05\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u8be5\u53d8\u91cf\u5bf9\u623f\u4ef7\u6709\u663e\u8457\u5f71\u54cd\u3002<\/p>\n<\/p>\n
\u516d\u3001\u603b\u7ed3<\/h3>\n<\/p>\n
\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u5982\u4f55\u4f7f\u7528Python\u53ca\u5176\u76f8\u5173\u5e93\u6765\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790\uff0c\u5e76\u83b7\u53d6t\u503c\u548cp\u503c\u3002\u6211\u4eec\u9996\u5148\u51c6\u5907\u4e86\u6570\u636e\uff0c\u7136\u540e\u4f7f\u7528statsmodels\u5e93\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790\uff0c\u6700\u540e\u83b7\u53d6\u5e76\u89e3\u91ca\u4e86t\u503c\u548cp\u503c\u3002\u8fd9\u4e9b\u6b65\u9aa4\u548c\u65b9\u6cd5\u5728\u5b9e\u9645\u6570\u636e\u5206\u6790\u4e2d\u5177\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u5e0c\u671b\u5bf9\u8bfb\u8005\u6709\u6240\u5e2e\u52a9\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5982\u4f55\u5728Python\u4e2d\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790\u4ee5\u83b7\u53d6t\u503c\u548cp\u503c\uff1f<\/strong>
\u8981\u83b7\u53d6t\u503c\u548cp\u503c\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528statsmodels<\/code>\u5e93\u8fdb\u884cOLS\u56de\u5f52\u5206\u6790\u3002\u9996\u5148\uff0c\u60a8\u9700\u8981\u5bfc\u5165\u6240\u9700\u7684\u5e93\uff0c\u5e76\u51c6\u5907\u60a8\u7684\u6570\u636e\u96c6\u3002\u4f7f\u7528OLS<\/code>\u51fd\u6570\u62df\u5408\u6a21\u578b\u540e\uff0c\u53ef\u4ee5\u901a\u8fc7summary()<\/code>\u51fd\u6570\u67e5\u770b\u7ed3\u679c\uff0c\u5176\u4e2d\u5305\u62ect\u503c\u548cp\u503c\u3002<\/p>\n
OLS\u56de\u5f52\u4e2dt\u503c\u548cp\u503c\u7684\u610f\u4e49\u662f\u4ec0\u4e48\uff1f<\/strong>
t\u503c\u662f\u7528\u4e8e\u68c0\u9a8c\u56de\u5f52\u7cfb\u6570\u662f\u5426\u663e\u8457\u4e0d\u540c\u4e8e\u96f6\u7684\u7edf\u8ba1\u91cf\u3002p\u503c\u5219\u8868\u793a\u5728\u5047\u8bbe\u68c0\u9a8c\u4e2d\u89c2\u5bdf\u5230\u7684\u7ed3\u679c\u6216\u66f4\u6781\u7aef\u7ed3\u679c\u7684\u6982\u7387\u3002\u901a\u5e38\uff0c\u5f53p\u503c\u5c0f\u4e8e0.05\u65f6\uff0c\u53ef\u4ee5\u8ba4\u4e3a\u8be5\u56de\u5f52\u7cfb\u6570\u5728\u7edf\u8ba1\u4e0a\u663e\u8457\u3002<\/p>\n
\u5982\u4f55\u89e3\u91caOLS\u56de\u5f52\u8f93\u51fa\u4e2d\u7684t\u503c\u548cp\u503c\uff1f<\/strong>
\u5728OLS\u56de\u5f52\u7684\u8f93\u51fa\u4e2d\uff0ct\u503c\u8d8a\u5927\uff0c\u8bf4\u660e\u56de\u5f52\u7cfb\u6570\u8d8a\u663e\u8457\u3002p\u503c\u8d8a\u5c0f\uff0c\u8868\u793a\u8be5\u7cfb\u6570\u4e0e\u96f6\u7684\u5dee\u5f02\u8d8a\u663e\u8457\u3002\u901a\u5e38\uff0cp\u503c\u5c0f\u4e8e0.05\u88ab\u89c6\u4e3a\u663e\u8457\uff0c\u8fd9\u610f\u5473\u7740\u53ef\u4ee5\u62d2\u7edd\u539f\u5047\u8bbe\uff0c\u8ba4\u4e3a\u8be5\u81ea\u53d8\u91cf\u5bf9\u56e0\u53d8\u91cf\u6709\u663e\u8457\u5f71\u54cd\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5982\u4f55\u5f97\u5230Python OLS\u7684t\u503cp\u503c \u5728\u4f7f\u7528Python\u8fdb\u884c\u7edf\u8ba1\u5206\u6790\u65f6\uff0c\u83b7\u53d6OLS\uff08\u666e\u901a\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09\u56de\u5f52\u6a21\u578b […]","protected":false},"author":3,"featured_media":1121871,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1121857"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1121857"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1121857\/revisions"}],"predecessor-version":[{"id":1121875,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1121857\/revisions\/1121875"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1121871"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1121857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1121857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1121857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}