最新2022年全國(guó)高考數(shù)學(xué)試題分類匯編§11.4 變量間的相關(guān)關(guān)系與統(tǒng)計(jì)案例

1、最新2022年全國(guó)高考數(shù)學(xué)試題分類匯編11.4 變量間的相關(guān)關(guān)系與統(tǒng)計(jì)案例of rural drinking water sources, protection of drinking water sources in rural areas by the end of the delimitation of the scope of protection, complete with warning signs, isolating network protection facilitiesof rural drinking water sources, protection of drin

2、king water sources in rural areas by the end of the delimitation of the scope of protection, complete with warning signs, isolating network protection facilitiesof rural drinking water sources, protection of drinking water sources in rural areas by the end of the delimitation of the scope of protect

3、ion, complete with warning signs, isolating network protection facilities11.4變量間的相關(guān)關(guān)系與統(tǒng)計(jì)案例考點(diǎn)一 變量間的相關(guān)關(guān)系1.(2022湖北,4,5分)變量x和y滿足關(guān)系y=-0.1x+1,變量y與z正相關(guān).以下結(jié)論中正確的選項(xiàng)是()A.x與y正相關(guān),x與z負(fù)相關(guān)B.x與y正相關(guān),x與z正相關(guān)C.x與y負(fù)相關(guān),x與z負(fù)相關(guān)D.x與y負(fù)相關(guān),x與z正相關(guān)答案C8.(2022課標(biāo),19,12分)某公司為確定下一年度投入某種產(chǎn)品的宣傳費(fèi),需了解年宣傳費(fèi)x(單位:千元)對(duì)年銷售量y(單位:t)和年利潤(rùn)z(單位:千元)的影

4、響.對(duì)近8年的年宣傳費(fèi)xi和年銷售量yi(i=1,2,8)數(shù)據(jù)作了初步處理,得到下面的散點(diǎn)圖及一些統(tǒng)計(jì)量的值.(xi-)2(wi-)2(xi-)(yi-)(wi-)(yi-)46.65636.8289.81.61 469108.8表中wi=,=wi.(1)根據(jù)散點(diǎn)圖判斷,y=a+bx與y=c+d哪一個(gè)適宜作為年銷售量y關(guān)于年宣傳費(fèi)x的回歸方程類型?(給出判斷即可,不必說(shuō)明理由)(2)根據(jù)(1)的判斷結(jié)果及表中數(shù)據(jù),建立y關(guān)于x的回歸方程;(3)這種產(chǎn)品的年利潤(rùn)z與x,y的關(guān)系為z=0.2y-x.根據(jù)(2)的結(jié)果答復(fù)以下問(wèn)題:(i)年宣傳費(fèi)x=49時(shí),年銷售量及年利潤(rùn)的預(yù)報(bào)值是多少?(ii)年宣

5、傳費(fèi)x為何值時(shí),年利潤(rùn)的預(yù)報(bào)值最大?附:對(duì)于一組數(shù)據(jù)(u1,v1),(u2,v2),(un,vn),其回歸直線v=+u的斜率和截距的最小二乘估計(jì)分別為=,=- .解析(1)由散點(diǎn)圖可以判斷,y=c+d適宜作為年銷售量y關(guān)于年宣傳費(fèi)x的回歸方程類型.(2分)(2)令w=,先建立y關(guān)于w的線性回歸方程.由于=68,=- =563-686.8=100.6,所以y關(guān)于w的線性回歸方程為=100.6+68w,因此y關(guān)于x的回歸方程為=100.6+68.(6分)(3)(i)由(2)知,當(dāng)x=49時(shí),年銷售量y的預(yù)報(bào)值=100.6+68=576.6,年利潤(rùn)z的預(yù)報(bào)值=576.60.2-49=66.32.(9

6、分)(ii)根據(jù)(2)的結(jié)果知,年利潤(rùn)z的預(yù)報(bào)值=0.2(100.6+68)-x=-x+13.6+20.12.所以當(dāng)=6.8,即x=46.24時(shí),取得最大值.故年宣傳費(fèi)為46.24千元時(shí),年利潤(rùn)的預(yù)報(bào)值最大.(12分)9.(2022重慶,17,13分)隨著我國(guó)經(jīng)濟(jì)的開(kāi)展,居民的儲(chǔ)蓄存款逐年增長(zhǎng).設(shè)某地區(qū)城鄉(xiāng)居民人民幣儲(chǔ)蓄存款(年底余額)如下表:年份20222022202220222022時(shí)間代號(hào)t12345儲(chǔ)蓄存款y(千億元)567810 (1)求y關(guān)于t的回歸方程=t+;(2)用所求回歸方程預(yù)測(cè)該地區(qū)2022年(t=6)的人民幣儲(chǔ)蓄存款.附:回歸方程=t+中,=-.解析(1)列表計(jì)算如下:itiyitiyi11515226412337921448163255102550153655120這里n=5,=ti=3,=yi=7.2.又ltt=-n=55-532=10,lty=tiyi-n=120-537