Positive Correlation but Negative correlation in Regression.

  • When conducting 6 simple correlations between government spending policies and Bolivia's living standards it results in a positive correlation.
    All six have a positive correlation.


    However when I conduct a regression with other variables Crime, Sanitation and Housing become negative:


    [TABLE="width: 491"]

    [tr]


    [td][/td]


    [td]

    Coefficients

    [/td]


    [td]

    Standard Error

    [/td]


    [td]

    t Stat

    [/td]


    [td]

    P-value

    [/td]


    [/tr]


    [tr]


    [td]

    Intercept

    [/td]


    [TD="align: right"]6.823557676[/TD]
    [TD="align: right"]0.295532403[/TD]
    [TD="align: right"]23.08903388[/TD]
    [TD="align: right"]2.68566E-65[/TD]

    [/tr]


    [tr]


    [td]

    Health

    [/td]


    [TD="align: right"]0.417455289[/TD]
    [TD="align: right"]0.225160128[/TD]
    [TD="align: right"]1.854037364[/TD]
    [TD="align: right"]0.064849087[/TD]

    [/tr]


    [tr]


    [td]

    Crime

    [/td]


    [TD="align: right"]-0.306447043[/TD]
    [TD="align: right"]0.115718489[/TD]
    [TD="align: right"]-2.648211587[/TD]
    [TD="align: right"]0.00857905[/TD]

    [/tr]


    [tr]


    [td]

    Education

    [/td]


    [TD="align: right"]1.072571017[/TD]
    [TD="align: right"]0.196736177[/TD]
    [TD="align: right"]5.451824039[/TD]
    [TD="align: right"]1.14478E-07[/TD]

    [/tr]


    [tr]


    [td]

    Sanitation

    [/td]


    [TD="align: right"]-0.472792444[/TD]
    [TD="align: right"]0.134749317[/TD]
    [TD="align: right"]-3.508681564[/TD]
    [TD="align: right"]0.00052923[/TD]

    [/tr]


    [tr]


    [td]

    Housing

    [/td]


    [TD="align: right"]-0.525306325[/TD]
    [TD="align: right"]0.246285809[/TD]
    [TD="align: right"]-2.132913497[/TD]
    [TD="align: right"]0.033854353[/TD]

    [/tr]


    [tr]


    [td]

    Welfare

    [/td]


    [TD="align: right"]0.350597928[/TD]
    [TD="align: right"]0.169207021[/TD]
    [TD="align: right"]2.072005789[/TD]
    [TD="align: right"]0.039235858[/TD]

    [/tr]


    [/TABLE]


    Why is this?


    Is this a problem with my regression?


    Or is it simply the variables interacting with each other?

  • Multicollinearity issue, does it make my results insignificant?


    I have conducted a regression where 6 out of 9 explanatory variables are marked on the same scale of 0 to 5. Excerpt from data seen below.
    [TABLE="width: 384"]

    [tr]


    [TD="class: xl64, width: 64, align: right"]1[/TD]
    [TD="class: xl65, width: 64, align: right"]2[/TD]
    [TD="class: xl65, width: 64, align: right"]3[/TD]
    [TD="class: xl65, width: 64, align: right"]4[/TD]
    [TD="class: xl65, width: 64, align: right"]5[/TD]
    [TD="class: xl64, width: 64, align: right"]6[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.7945709[/TD]
    [TD="class: xl63, align: right"]2.523261[/TD]
    [TD="class: xl63, align: right"]2.768621[/TD]
    [TD="class: xl63, align: right"]3.12227[/TD]
    [TD="class: xl63, align: right"]2.537218[/TD]
    [TD="align: right"]2.287279[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.6657027[/TD]
    [TD="class: xl63, align: right"]2.318319[/TD]
    [TD="class: xl63, align: right"]2.883092[/TD]
    [TD="class: xl63, align: right"]3.089985[/TD]
    [TD="class: xl63, align: right"]2.463932[/TD]
    [TD="align: right"]2.315841[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.8066551[/TD]
    [TD="class: xl63, align: right"]2.54824[/TD]
    [TD="class: xl63, align: right"]2.556541[/TD]
    [TD="class: xl63, align: right"]2.785207[/TD]
    [TD="class: xl63, align: right"]2.300211[/TD]
    [TD="align: right"]2.161496[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.6643963[/TD]
    [TD="class: xl63, align: right"]1.641753[/TD]
    [TD="class: xl63, align: right"]2.239954[/TD]
    [TD="class: xl63, align: right"]1.562361[/TD]
    [TD="class: xl63, align: right"]1.682554[/TD]
    [TD="align: right"]1.985844[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.8280855[/TD]
    [TD="class: xl63, align: right"]2.119587[/TD]
    [TD="class: xl63, align: right"]2.490479[/TD]
    [TD="class: xl63, align: right"]1.780684[/TD]
    [TD="class: xl63, align: right"]1.679536[/TD]
    [TD="align: right"]1.977059[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.8393802[/TD]
    [TD="class: xl63, align: right"]1.929261[/TD]
    [TD="class: xl63, align: right"]2.479487[/TD]
    [TD="class: xl63, align: right"]1.804895[/TD]
    [TD="class: xl63, align: right"]1.673621[/TD]
    [TD="align: right"]2.045525[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.7411508[/TD]
    [TD="class: xl63, align: right"]2.486125[/TD]
    [TD="class: xl63, align: right"]2.411711[/TD]
    [TD="class: xl63, align: right"]1.931177[/TD]
    [TD="class: xl63, align: right"]1.918335[/TD]
    [TD="align: right"]2.069157[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.8605461[/TD]
    [TD="class: xl63, align: right"]2.517329[/TD]
    [TD="class: xl63, align: right"]2.46032[/TD]
    [TD="class: xl63, align: right"]1.837561[/TD]
    [TD="class: xl63, align: right"]1.897486[/TD]
    [TD="align: right"]2.102621[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.9125756[/TD]
    [TD="class: xl63, align: right"]2.622658[/TD]
    [TD="class: xl63, align: right"]2.469014[/TD]
    [TD="class: xl63, align: right"]1.804663[/TD]
    [TD="class: xl63, align: right"]1.866855[/TD]
    [TD="align: right"]2.10192[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.8072717[/TD]
    [TD="class: xl63, align: right"]2.426955[/TD]
    [TD="class: xl63, align: right"]2.371158[/TD]
    [TD="class: xl63, align: right"]1.765089[/TD]
    [TD="class: xl63, align: right"]1.799954[/TD]
    [TD="align: right"]2.026291[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.7447101[/TD]
    [TD="class: xl63, align: right"]2.264876[/TD]
    [TD="class: xl63, align: right"]2.173995[/TD]
    [TD="class: xl63, align: right"]1.656273[/TD]
    [TD="class: xl63, align: right"]1.79111[/TD]
    [TD="align: right"]1.9964[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.8302365[/TD]
    [TD="class: xl63, align: right"]2.412752[/TD]
    [TD="class: xl63, align: right"]2.309863[/TD]
    [TD="class: xl63, align: right"]1.741599[/TD]
    [TD="class: xl63, align: right"]1.87927[/TD]
    [TD="align: right"]2.086493[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.8156909[/TD]
    [TD="class: xl63, align: right"]2.639425[/TD]
    [TD="class: xl63, align: right"]2.363351[/TD]
    [TD="class: xl63, align: right"]1.778991[/TD]
    [TD="class: xl63, align: right"]1.9125[/TD]
    [TD="align: right"]2.098853[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.7576525[/TD]
    [TD="class: xl63, align: right"]2.583813[/TD]
    [TD="class: xl63, align: right"]2.245098[/TD]
    [TD="class: xl63, align: right"]1.53905[/TD]
    [TD="class: xl63, align: right"]1.785954[/TD]
    [TD="align: right"]2.012423[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.7367484[/TD]
    [TD="class: xl63, align: right"]2.545393[/TD]
    [TD="class: xl63, align: right"]2.210216[/TD]
    [TD="class: xl63, align: right"]1.51596[/TD]
    [TD="class: xl63, align: right"]1.768283[/TD]
    [TD="align: right"]2.039025[/TD]

    [/tr]


    [tr]


    [TD="class: xl66, align: right"]2.7936911[/TD]
    [TD="class: xl63, align: right"]2.575252[/TD]
    [TD="class: xl63, align: right"]2.317997[/TD]
    [TD="class: xl63, align: right"]1.421082[/TD]
    [TD="class: xl63, align: right"]1.594394[/TD]
    [TD="align: right"]1.919797[/TD]

    [/tr]


    [/TABLE]



    Due to them also being correlated (See below) is this a serious multicollinearty issue that means my regressio results are insignificant? (see below)
    Variable 1 & 2 =0.817846
    Variable 2 & 3 = 0.62312
    Variable 3 & 4 = 0.842107
    Variable 4 & 5 = 0.844526
    Variable 5 & 6 = 0.929187


    Regression results
    [TABLE="width: 499"]

    [tr]


    [td][/td]


    [td]

    Coefficients

    [/td]


    [td]

    Standard Error

    [/td]


    [td]

    t Stat

    [/td]


    [td]

    P-value

    [/td]


    [/tr]


    [tr]


    [td]

    Intercept

    [/td]


    [TD="align: right"]7.657114437[/TD]
    [TD="align: right"]0.320950828[/TD]
    [TD="align: right"]23.85759368[/TD]
    [TD="align: right"]1.56203E-67[/TD]

    [/tr]


    [tr]


    [td]

    1

    [/td]


    [TD="align: right"]0.401967263[/TD]
    [TD="align: right"]0.201176626[/TD]
    [TD="align: right"]1.998081344[/TD]
    [TD="align: right"]0.04674538[/TD]

    [/tr]


    [tr]


    [td]

    2

    [/td]


    [TD="align: right"]-0.149847228[/TD]
    [TD="align: right"]0.104101885[/TD]
    [TD="align: right"]-1.439428579[/TD]
    [TD="align: right"]0.15122738[/TD]

    [/tr]


    [tr]


    [td]

    3

    [/td]


    [TD="align: right"]0.848281878[/TD]
    [TD="align: right"]0.176776938[/TD]
    [TD="align: right"]4.798600358[/TD]
    [TD="align: right"]2.69132E-06[/TD]

    [/tr]


    [tr]


    [td]

    4

    [/td]


    [TD="align: right"]-0.396603539[/TD]
    [TD="align: right"]0.133370769[/TD]
    [TD="align: right"]-2.973691619[/TD]
    [TD="align: right"]0.003217662[/TD]

    [/tr]


    [tr]


    [td]

    5

    [/td]


    [TD="align: right"]-0.36444739[/TD]
    [TD="align: right"]0.220129689[/TD]
    [TD="align: right"]-1.655603071[/TD]
    [TD="align: right"]0.099004046[/TD]

    [/tr]


    [tr]


    [td]

    6

    [/td]


    [TD="align: right"]0.078668917[/TD]
    [TD="align: right"]0.164035587[/TD]
    [TD="align: right"]0.479584453[/TD]
    [TD="align: right"]0.631924521[/TD]

    [/tr]


    [tr]


    [td]

    7

    [/td]


    [TD="align: right"]-0.145393714[/TD]
    [TD="align: right"]0.086736012[/TD]
    [TD="align: right"]-1.676278527[/TD]
    [TD="align: right"]0.094881019[/TD]

    [/tr]


    [tr]


    [td]

    8

    [/td]


    [TD="align: right"]1.47872E-11[/TD]
    [TD="align: right"]3.26495E-12[/TD]
    [TD="align: right"]4.52907424[/TD]
    [TD="align: right"]9.01855E-06[/TD]

    [/tr]


    [tr]


    [td]

    9

    [/td]


    [TD="align: right"]-0.005853495[/TD]
    [TD="align: right"]0.001110117[/TD]
    [TD="align: right"]-5.272863884[/TD]
    [TD="align: right"]2.81956E-07[/TD]

    [/tr]


    [/TABLE]


    [TABLE="width: 384"]

    [tr]


    [TD="width: 64, align: right"][/TD]
    [TD="width: 64, align: right"][/TD]
    [TD="width: 64, align: right"][/TD]
    [TD="width: 64, align: right"][/TD]
    [TD="width: 64, align: right"][/TD]
    [TD="width: 64, align: right"][/TD]

    [/tr]


    [/TABLE]