linear model

直線回帰モデル、直線モデル、線形回帰モデル

関

linear regression

WordNet

1. mark with lines; "sorrow had lined his face"
2. a length (straight or curved) without breadth or thickness; the trace of a moving point
3. a single frequency (or very narrow band) of radiation in a spectrum
4. reinforce with fabric; "lined books are more enduring"
5. a particular kind of product or merchandise; "a nice line of shoes" (同)product line, line of products, line of merchandise, business line, line of business
6. the road consisting of railroad track and roadbed (同)railway line, rail line
7. a commercial organization serving as a common carrier
8. acting in conformity; "in line with"; "he got out of line"; "toe the line"
9. something (as a cord or rope) that is long and thin and flexible; "a washing line"
10. a conceptual separation or distinction; "there is a narrow line between sanity and insanity" (同)dividing_line, demarcation, contrast
11. a formation of people or things one behind another; "the line stretched clear around the corner"; "you must wait in a long line at the checkout counter"
12. a formation of people or things one beside another; "the line of soldiers advanced with their bayonets fixed"; "they were arrayed in line of battle"; "the cast stood in line for the curtain call"
13. a fortified position (especially one marking the most forward position of troops); "they attacked the enemys line"
14. a mark that is long relative to its width; "He drew a line on the chart"
15. a spatial location defined by a real or imaginary unidimensional extent
16. in games or sports; a mark indicating positions or bounds of the playing area
17. persuasive but insincere talk that is usually intended to deceive or impress; "`let me show you my etchings is a rather worn line"; "he has a smooth line but I didnt fall for it"; "that salesman must have practiced his fast line of talk"
18. text consisting of a row of words written across a page or computer screen; "the letter consisted of three short lines"; "there are six lines in every stanza"
19. be in line with; form a line along; "trees line the riverbank" (同)run along
20. cover the interior of; "line the gloves"; "line a chimney"
21. fill plentifully; "line ones pockets"
22. display (clothes) as a mannequin; "model the latest fashion"
23. the act of representing something (usually on a smaller scale) (同)modelling, modeling
24. representation of something (sometimes on a smaller scale) (同)simulation
25. a representative form or pattern; "I profited from his example" (同)example
26. a person who poses for a photographer or painter or sculptor; "the president didnt have time to be a model so the artist worked from photos" (同)poser
27. someone worthy of imitation; "every child needs a role model" (同)role model
28. a hypothetical description of a complex entity or process; "the computer program was based on a model of the circulatory and respiratory systems" (同)theoretical account, framework
29. a type of product; "his car was an old model"
30. construct a model of; "model an airplane" (同)mock up
31. form in clay, wax, etc; "model a head with clay" (同)mold, mould
32. plan or create according to a model or models (同)pattern
33. assume a posture as for artistic purposes; "We dont know the woman who posed for Leonardo so often" (同)pose, sit, posture
34. create a representation or model of; "The pilots are trained in conditions simulating high-altitude flights" (同)simulate
35. measured lengthwise; "cost of lumber per running foot" (同)running
36. designating or involving an equation whose terms are of the first degree (同)additive
37. (of a leaf shape) long and narrow (同)elongate
38. of or in or along or relating to a line; involving a single dimension; "a linear measurement" (同)one-dimensional
39. a particular functioning condition or arrangement; "switched from keyboard to voice mode"
40. the most frequent value of a random variable (同)modal value
41. any of various fixed orders of the various diatonic notes within an octave (同)musical mode
42. relating to a recently developed fashion or style; "their offices are in a modern skyscraper"; "tables in modernistic designs"; (同)modern, modernistic
43. a British teenager or young adult in the 1960s; noted for their clothes consciousness and opposition to the rockers

PrepTutorEJDIC

1. 『線』,筋,けい / (色・縫い目などの)『線』,しま;(顔・手などの)しわ(wrinkle) / (物・人の)『列』,行列(row) / 『綱』,糸,針金 / 電線,電話線,電信線 / (文章の)『行』;(詩の)『行』 / 《しばしばa~》《話》『短い手紙』(note) / 《複数形で》輪郭,外形(outline) / 境界線(boundary);限界,限度(limit) / (鉄道・バスなどの)路線;航路,空路 / 《複数形で》せりふ / 進路,道順(course);(考えなどの)筋道,方針 / 《しばしばone's~》(活動の)分野,方面;特意 / 家系,血統,血筋 / 在庫商品,仕入れ品 / 導管,パイプライン / 《しばしば複数形で》戦線,防御線 / …‘に'『線を引く』,筋(しま,しわ)をつける / …‘に'『沿って並ぶ;』(…を)…‘に'沿って並べる《+『名』+『with』+『名』》
2. (材料で)〈着物など〉‘に'裏を付ける《+『名』『with』+『名』》 / (…で)…‘を'満たす,(…を)…‘に'詰め込む《+『名』+『with』+『名』》
3. (通名縮小した)(…の)『模型』,ひな型《+『of』+『名』》 / 《単数形で》(…の)『模範』,手本《+『of』+(『for』)+『名』》 / (美術家・作家などの)モデル,ファッションモデル / (自動車・服装などの)型,式《+『of』+『名』》 / 《英》《単数形で》(…と)そっくりな人(物),(…の)生き写し《+『of』+『名』》 / 『模型の』,見本の / 『日範的な』,申し分のない / (ある材料で)…‘の'模型を作る,‘を'型どる《+『名』+『in』+『名』〈材料〉》 / (手本・型に合わせて)…‘を'作る《+『名』+『after』(『on, upon』)+『名』(a person's do『ing』)》 / 〈洋装・髪型などの〉‘の'モデルをする / (…で)(原型)を作る《+『in』+『名』》 / (ファッションショーなどで)モデルをする
4. 線の,直線の / 線から成る,線を使った;線状の / (方程式が)一次の
5. 〈C〉(…の)『方法』,やり方,流儀《+『of』+『名』(do『ing』)》 / 〈U〉〈C〉(服装などの)『流行』,モード / 〈C〉(動詞の)法,叙法(mood) / 音階(scale)
6. モッズふうな(服装・音楽などについて伝統にとらわれない考え方の一つ)[modernの短縮形]

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/05/30 23:13:24」(JST)

wiki en

[Wiki en表示]

Not to be confused with linear model of innovation.

In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning. In each case, the designation "linear" is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.

Linear regression models

For the regression case, the statistical model is as follows. Given a (random) sample the relation between the observations Y_i and the independent variables X_ij is formulated as

where may be nonlinear functions. In the above, the quantities ε_i are random variables representing errors in the relationship. The "linear" part of the designation relates to the appearance of the regression coefficients, β_j in a linear way in the above relationship. Alternatively, one may say that the predicted values corresponding to the above model, namely

are linear functions of the β_j.

Given that estimation is undertaken on the basis of a least squares analysis, estimates of the unknown parameters β_j are determined by minimising a sum of squares function

From this, it can readily be seen that the "linear" aspect of the model means the following:

• the function to be minimised is a quadratic function of the β_j for which minimisation is a relatively simple problem;
• the derivatives of the function are linear functions of the β_j making it easy to find the minimising values;
• the minimising values β_j are linear functions of the observations Y_i;
• the minimising values β_j are linear functions of the random errors ε_i which makes it relatively easy to determine the statistical properties of the estimated values of β_j.

Time series models

An example of a linear time series model is an autoregressive moving average model. Here the model for values {X_t} in a time series can be written in the form

where again the quantities ε_t are random variables representing innovations which are new random effects that appear at a certain time but also affect values of X at later times. In this instance the use of the term "linear model" refers to the structure of the above relationship in representing X_t as a linear function of past values of the same time series and of current and past values of the innovations. This particular aspect of the structure means that it is relative simple to derive relations for the mean and covariance properties of the time series. Note that here the "linear" part of the term "linear model" is not referring to the coefficients φ_i and θ_i, as it would be in the case of a regression model, which looks structurally similar.

Other uses in statistics

There are some other instances where "nonlinear model" is used to contrast with a linearly structured model, although the term "linear model" is not usually applied. One example of this is nonlinear dimensionality reduction.

See also

• General linear model
• Linear system
• Statistical model

References

UpToDate Contents

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English Journal

• Pulse pressure amplification and its determinants.

• Pichler G1, Martinez F1,2, Vicente A1, Solaz E1, Calaforra O1,2, Redon J1,2.
• Blood pressure.Blood Press.2016 Feb;25(1):1-7. doi: 10.3109/08037051.2015.1090713.
• BACKGROUND: Pulse pressure (PP) amplification expressed as the peripheral-to-central PP ratio has gained importance in the assessment of cardiovascular phenotypes and cardiovascular risk. The aim of the present study was to assess the relationship between PP amplification, large vessel parameters an
• PMID 26414776

• Adulteration of Argentinean milk fats with animal fats: Detection by fatty acids analysis and multivariate regression techniques.

• Rebechi SR1, Vélez MA2, Vaira S3, Perotti MC2.
• Food chemistry.Food Chem.2016 Feb 1;192:1025-32. doi: 10.1016/j.foodchem.2015.07.107. Epub 2015 Jul 23.
• The aims of the present study were to test the accuracy of the fatty acid ratios established by the Argentinean Legislation to detect adulterations of milk fat with animal fats and to propose a regression model suitable to evaluate these adulterations. For this purpose, 70 milk fat, 10 tallow and 7
• PMID 26304443

• Simultaneous spectrophotometric determination of copper, cobalt, nickel and iron in foodstuffs and vegetables with a new bis thiosemicarbazone ligand using chemometric approaches.

• Rohani Moghadam M1, Poorakbarian Jahromi SM2, Darehkordi A2.
• Food chemistry.Food Chem.2016 Feb 1;192:424-31. doi: 10.1016/j.foodchem.2015.07.029. Epub 2015 Jul 8.
• A newly synthesized bis thiosemicarbazone ligand, (2Z,2'Z)-2,2'-((4S,5R)-4,5,6-trihydroxyhexane-1,2-diylidene)bis(N-phenylhydrazinecarbothioamide), was used to make a complex with Cu(2+), Ni(2+), Co(2+) and Fe(3+) for their simultaneous spectrophotometric determination using chemometric methods. By
• PMID 26304369

Japanese Journal

• 鋼構造2層純骨組小模型の振動台実験の地震波加振レベルの違いによる応答比較

• 広島工業大学紀要. 研究編 42, 207-213, 39479-00-00
• NAID 120005403291

• Optimistic Value Model of Uncertain Linear Quadratic Optimal Control with Jump

• Journal of advanced computational intelligence and intelligent informatics 20(2), 189-196, 2016-03
• NAID 40020763427

• A Three Dimensional Model of the Real Special Linear Group of Degree Two and its Applications

• 東海大学紀要. 理学部 Proceedings of the School of Science of Tokai University 51, 1-10, 2016-03
• NAID 40020763075

Related Links

• Linear model - Wikipedia, the free encyclopedia

In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the ...

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リンク元	「linear regression」「直線回帰モデル」「直線モデル」「線形回帰モデル」
関連記事	「linear」「line」「mode」「model」

「linear regression」

　　[★]

• n.

• 直線回帰、線形回帰

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直線回帰 : 約 13,900 件
線形回帰 : 約 59,300 件

関

linear model

「直線回帰モデル」

　　[★]

英

linear model

関

直線回帰、直線モデル、線形回帰モデル

「直線モデル」

　　[★]

英

linear model

関

直線回帰モデル、線形回帰モデル

「線形回帰モデル」

　　[★]

英

linear model

関

直線回帰モデル、直線モデル

「linear」

　　[★]

• adj.

• 直線的な、直鎖状の、リニアな、(数学)線形の、比例した

関

linearly、normal、proportion、proportional、proportionally、proportionate、proportionately、straight

　 　 　 　 　

「line」

　　[★]

• n.

• 線、ライン、系統

• v.

• 裏打ちする

関

lineage、lining、pedigree、stock、strain、string、undercoat

　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　

「mode」

　　[★]

• n.

• モード、型、機序、方法

関

fashion、form、manner、means、mechanism、method、pattern、procedure、process、type、typed、way

　 　 　 　

「model」

　　[★]

• n.

• モデル、模型