---
# System prepended metadata

title: Columns

---

- ANOVA TABLE
    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FeCABvsW447.png?alt=media&token=22021019-15e1-458b-a564-10413c222300)
    - # Columns
        - Degrees of Freedom
        - Sum of squares
        - Mean of Squares
        - F value / F statistic / F-ratio
        - pr bullshit
    - # Stats
        - F ratio
            - Found in column
        - Critical value
            - `qf(sig_value, df, df)`
            - **IF THE F RATIO IS GREATER THAN THE CRIT VALUE, REJECT** $$H_0$$
            - **IF PR_BULLSHIT IS LESS THAN SIG_VALUE, REJECT ** $$H_0$$
    - # FINDING A, B, C, D
        - A
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2F3iXcOAMNmh.png?alt=media&token=bc27c456-b393-42a1-b565-f796de96508f)
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FM8S0-4FS-r.png?alt=media&token=9af035c2-601d-4165-8db8-3915499ff4f8)
        - B
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2Fk4Vub_MwqX.png?alt=media&token=691ed181-fffb-4ac7-a7b0-779130ac62f0)
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FRy1GG-Y67h.png?alt=media&token=415922db-c48f-491a-97fc-fe48de03235f)
        - C
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FtQE70cXUMX.png?alt=media&token=f3e3713b-3a9c-4e8d-86f4-dec7e6591c34)
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2Fua5Kcg_HTx.png?alt=media&token=1a639a05-d15d-41fb-a47e-b4c597065924)
        - D
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FWyH_Dq63CH.png?alt=media&token=ce1e16e6-0768-4188-bfff-7f0c9d5bdeb3)
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2F6jNrst_idM.png?alt=media&token=a71ae7a5-74d1-44a6-9cd2-08479ef36371)
    - # TYPES OF MODELS
        - REDUCED MODEL
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2F_s4S84MV1k.png?alt=media&token=e5daf94f-9a69-4f48-8e47-407c99bbd4e8)
            - STATS
                - µ
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FdlOmP6Sv3x.png?alt=media&token=02b41285-37bd-4dec-990a-5a7a9942fe01)
                    - 5 PLUS SAMPLE MEAN 1, 5 + SAMPLE MEAN 2, ETC ETC
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2Fq_KU8wZoak.png?alt=media&token=adf7f13d-7888-4c08-828b-bef84acc2794)
                - $$σ^2$$
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FXDcR3eV7Kx.png?alt=media&token=d70c3f96-5eaa-4407-9291-dcd4981a242c)
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2F_-dgi3jtBw.png?alt=media&token=059fc9a2-6c1b-4438-be6f-7105a190571b)
                - RESIDUAL SUM OF SQUARES
                    - RIGHT HERE:
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FCRUseiyYyF.png?alt=media&token=aaf4367a-5479-4a21-ba1e-67f4bd024800)
        - FULL MODEL
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FdWrkkb1JFX.png?alt=media&token=a160c76c-4fdb-4047-94bb-8e6789fb847d)
            - STATS
                - $$σ^2$$
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2F9REr8SycKb.png?alt=media&token=f3935e27-686c-4233-9e24-14b5b5f12ebc)
                        - 4 TIMES SAMPLE VARIANCE1, 4 TIMES SAMPLE VARIANCE 2, ETC
                        - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2Ft62-J6vKlT.png?alt=media&token=685b5085-c913-4913-ac4d-6ccb354e27fa)
                    - IT IS ALSO JUST "A"
                        - HERE IT IS AGAIN
                        - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2Fu8SfSGzMpQ.png?alt=media&token=fbcdb433-47b2-4ace-b8bb-02c62c1b82ed)
                - RESIDUAL SUM OF SQUARES
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FJPkr3XPDXo.png?alt=media&token=2bd397d6-d0b7-4a7e-b20d-986a5506280b)
                    - SAME THING AS $$σ^2$$, BUT WITHOUT BEING DIVIDED BY 4 + 4+ ETC ETC
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2Ft62-J6vKlT.png?alt=media&token=685b5085-c913-4913-ac4d-6ccb354e27fa)
        - EXTRA SUM OF SQUARES
            - THIS USES BOTH MODELS
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FfBKMR1dd3B.png?alt=media&token=45f8451f-8369-45e5-8416-c7de8a52eb40)
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FsdJLsTzXrq.png?alt=media&token=9e4ab1c8-4cd5-49b9-a7f8-f665f80859fa)
            - IF THIS IS GREATER THAN ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2F22mnOpX3XJ.png?alt=media&token=2228e97d-e9b8-4fa1-bf63-d2f1927a781a) YOU WANT TO USE THE FULL MODEL
            - 3 TIMES "Critical value" TIMES RESIDUAL_SUMSQ
                - RESIDUAL_SUMSQ CAN BE FOUND HERE
                    - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FNhz-6Q33Pa.png?alt=media&token=83e78385-9d28-41a0-b1fa-6fb7e375e8b2)
            - 
    - # DIAGNOSTIC CHECKING
        - RESIDUALS
            - OBSERVATION - FITTED VALUE
        - RESIDUAL SUM OF SQUARES
            - A MEASURE OF HOW WELL THE MODEL FITS THE DATA
        - NORMALITY ASSUMPTION
            - MAKE SURE THE DATA FITS A BELL CURVE
            - USE THE HISTOGRAM AND QQ PLOT OF STANDARDISED RESIDUALS
            - QQ PLOT
                - IF THEY FIT ALONG THE LINE
        - CONSTANT VARIANCE ASSUMPTION
            - WHEN YOU PLOT THE INDIVIDUAL ERROR AGAINST PREDICTED VALUE, THE VARIANCE OF ERROR PREDICTED VALUE SHOULD BE CONSTANCT
            - ![](https://firebasestorage.googleapis.com/v0/b/firescript-577a2.appspot.com/o/imgs%2Fapp%2FInformal%2FF0io8SQwMd.png?alt=media&token=1bc858a7-4a9a-4842-9584-ac553ae41b07)
        - STANDARDISED RESIDUALS
            - IF GREATER THAN 2 OR LESS THAN -2 THEY ARE UNUSUAL OBSERVATIONS
            - CORRELATED VALUES
            - 
