\\(x\\) \u306f \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3067\u3042\u308b.\r\n\u6b21\u306e\u8868\u306f \\(2\\) \u3064\u306e\u79d1\u76ee X \u3068 Y \u306e\u8a66\u9a13\u3092\u53d7\u3051\u305f \\(5\\) \u4eba\u306e\u5f97\u70b9\u3092\u307e\u3068\u3081\u305f\u3082\u306e\u3067\u3042\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} & [1] & [2] & [3] & [4] & [5] \\\\ \\hline \\text{\u79d1\u76ee X \u306e\u5f97\u70b9} & x & 6 & 4 & 7 & 4 \\\\ \\hline \\text{\u79d1\u76ee Y \u306e\u5f97\u70b9} & 9 & 7 & 5 & 10 & 9 \\end{array}\r\n\\]\r\n
(1)<\/strong>\u3000\\(2n\\) \u500b\u306e\u5b9f\u6570 \\(a_1 , a_2 , \\cdots , a_n , b_1 , b_2 , \\cdots b_n\\) \u306b\u3064\u3044\u3066, \\(a = \\dfrac{1}{n} \\textstyle\\sum\\limits _ {k=1}^{n} a_k\\) , \\(b = \\dfrac{1}{n} \\textstyle\\sum\\limits _ {k=1}^{n} b_k\\) \u3068\u3059\u308b\u3068,\r\n\\[\r\n\\textstyle\\sum\\limits _ {k=1}^{n} ( a_k -a ) ( b_k -b ) = \\textstyle\\sum\\limits _ {k=1}^{n} a_k b_k -nab\r\n\\]\r\n\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n (2)<\/strong>\u3000\u79d1\u76ee X \u306e\u5f97\u70b9\u3068\u79d1\u76ee Y \u306e\u5f97\u70b9\u306e\u76f8\u95a2\u4fc2\u6570 \\(r_{XY}\\) \u3092 \\(x\\) \u3067\u8868\u305b.<\/p><\/li>\r\n (3)<\/strong>\u3000\\(x\\) \u306e\u5024\u3092 \\(2\\) \u5897\u3084\u3057\u3066 \\(r _{XY}\\) \u3092\u8a08\u7b97\u3057\u3066\u3082\u5024\u306f\u540c\u3058\u3067\u3042\u3063\u305f. \u3053\u306e\u3068\u304d, \\(r _{XY}\\) \u306e\u5024\u3092\u56db\u6368\u4e94\u5165\u3057\u3066\u5c0f\u6570\u7b2c \\(1\\) \u4f4d\u307e\u3067\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n (1)<\/strong><\/p>\r\n \\[\\begin{align}\r\n\\textstyle\\sum\\limits _ {k=1}^{n} ( a_k -a ) ( b_k -b ) & = \\textstyle\\sum\\limits _ {k=1}^{n} \\left( a_k b_k -b a_k -a b_k +ab \\right) \\\\\r\n& = \\textstyle\\sum\\limits _ {k=1}^{n} a_k b_k -nab -nab +nab \\\\\r\n& = \\textstyle\\sum\\limits _ {k=1}^{n} a_k b_k -nab\r\n\\end{align}\\]\r\n (2)<\/strong><\/p>\r\n \\(5\\) \u4eba\u306e X ,Y \u305d\u308c\u305e\u308c\u306e\u5f97\u70b9\u3092 \\(x_k , y_k \\ ( k = 1 , \\cdots , 5 )\\) \u3068\u3057\u3066, \u5e73\u5747\u3092 \\(\\overline{x} , \\overline{y}\\) , \u5206\u6563\u3092 \\({s_X}^2 , {s_Y}^2\\) , X \u3068 Y \u306e\u5171\u5206\u6563\u3092 \\(s _ {XY}\\) \u3068\u304a\u304f\u3068, (1)<\/strong> \u306e\u7d50\u679c\u3082\u7528\u3044\u3066\r\n\\[\\begin{align}\r\n\\overline{x} & = \\dfrac{x +21}{5} \\ , \\\\\r\n\\overline{y} & = \\dfrac{40}{5} = 8 \\ , \\\\\r\n{s_X}^2 & = \\dfrac{x^2 +36 +16 +49 +16}{5} -\\overline{x}^2 \\\\\r\n& = \\dfrac{x^2 +112}{5} -\\dfrac{(x +21)^2}{25} \\\\\r\n& = \\dfrac{4 x^2 -42x +144}{25} , \\\\\r\n{s_Y}^2 & = \\dfrac{81 +49 +25 +100 +81}{5} -\\overline{y}^2\\\\\r\n& = \\dfrac{336}{5} -64 = \\dfrac{16}{5} \\ , \\\\\r\ns _ {XY} & = \\dfrac{1}{5} \\textstyle\\sum\\limits _ {i=k}^{n} x_k y_k -\\overline{x} \\overline{y} \\\\\r\n& = \\dfrac{9x +42 +20 +70 +36}{5} -\\dfrac{x +21}{5} \\cdot 8 \\\\\r\n& = \\dfrac{9x +168}{5} -\\dfrac{8x +168}{5} \\\\\r\n& = \\dfrac{x}{5}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5024\u306f\r\n\\[\\begin{align}\r\nr_{XY} & = \\dfrac{s _ {XY}}{s_X s_Y} \\\\\r\n& = \\dfrac{\\dfrac{x}{5}}{\\dfrac{\\sqrt{4 x^2 -42x +144}}{5} \\cdot \\dfrac{4}{\\sqrt{5}}} \\\\\r\n& = \\underline{\\dfrac{\\sqrt{5} x}{4 \\sqrt{4 x^2 -42x +144}}}\r\n\\end{align}\\]\r\n (3)<\/strong><\/p>\r\n \u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{\\sqrt{5} x}{4 \\sqrt{4 x^2 -42x +144}} & = \\dfrac{\\sqrt{5} (x+2)}{4 \\sqrt{4 (x+2)^2 -42(x+2) +144}} \\\\\r\n5 x^2 ( 4 x^2 -26x +76 ) & = 5 (x+2)^2 ( 4 x^2 -42x +144 ) \\\\\r\n20 x^4 -130 x^3 +380 x^2 & = 20 x^4 -130x^3 +464 x^2 -408 x -576 \\\\\r\n7x^2 -34 x -48 & = 0 \\\\\r\n( x -6 ) ( 7x +8 ) & = 0 \\\\\r\n\\end{align}\\]\r\n\\(x\\) \u306f \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u306a\u306e\u3067\r\n\\[\r\nx = 6\r\n\\]\r\n\u3053\u306e\u3068\u304d, \\(\\sqrt{5} = 2.236 \\cdots\\) \u3092\u7528\u3044\u3066\r\n\\[\r\nr _{XY} = \\dfrac{6 \\sqrt{5}}{4 \\sqrt{36}} = \\dfrac{\\sqrt{5}}{4} = 0.559 \\cdots\r\n\\]\r\n\u306a\u306e\u3067, \u5c0f\u6570\u7b2c \\(2\\) \u4f4d\u3092\u56db\u6368\u4e94\u5165\u3057\u3066\r\n\\[\r\nr _{XY} = \\underline{0.6}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(x\\) \u306f \\(0\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3067\u3042\u308b. \u6b21\u306e\u8868\u306f \\(2\\) \u3064\u306e\u79d1\u76ee X \u3068 Y \u306e\u8a66\u9a13\u3092\u53d7\u3051\u305f \\(5\\) \u4eba\u306e\u5f97\u70b9\u3092\u307e\u3068\u3081\u305f\u3082\u306e\u3067\u3042\u308b. \\[ \\begin{array}{c|ccccc} & [1] & … \u7d9a\u304d\u3092\u8aad\u3080
\r\n\r\n\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n