https://firebase.google.com/products/analytics?hl=ja

全部の情報はいらないっぽいな
https://firebase.google.com/docs/reference/js/firebase

// Initialize default app
// Retrieve your own options values by adding a web app on
// https://console.firebase.google.com
firebase.initializeApp({
  apiKey: "AIza....",                             // Auth / General Use
  applicationId: "1:27992087142:web:ce....",      // General Use
  projectId: "my-firebase-project",               // General Use
  authDomain: "YOUR_APP.firebaseapp.com",         // Auth with popup/redirect
  databaseURL: "https://YOUR_APP.firebaseio.com", // Realtime Database
  storageBucket: "YOUR_APP.appspot.com",          // Storage
  messagingSenderId: "123456789"                  // Cloud Messaging
});

// Initialize another app
var otherApp = firebase.initializeApp({
  apiKey: "AIza....",
  applicationId: "1:27992087142:web:ce....",
  projectId: "my-firebase-project",
  databaseURL: "https://<OTHER_DATABASE_NAME>.firebaseio.com",
  storageBucket: "<OTHER_STORAGE_BUCKET>.appspot.com"
}, "nameOfOtherApp");

Vue CLiでプロジェクトを作成

$ npm install -g @vue/cli
$ vue create VueTest
$ cd VueTest
VueTest $ npm install firebase --save

main.jsに追加

import Vue from 'vue'
import App from './App.vue'

import * as firebase from "firebase/app";
import "firebase/analytics";

const firebaseConfig = {
  apiKey: 'xxxxxxxx',
  projectId: 'xxxxxx',
  appId: 'xxxxxx',
  measurementId: 'xxxxxx'
};

firebase.initializeApp(firebaseConfig);
firebase.analytics();

Vue.config.productionTip = false

// alias
Vue.prototype.$analytics = firebase.analytics();

new Vue({
  render: h => h(App),
}).$mount('#app')

• apiKey
• projectId
• appId
• measurementId

この4つがあれば大丈夫なことがわかった。