Confidence intervals interpretation help

Hi all! I have the following code:

Linear regression model:
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate      SE        tStat       pValue  
                   ________    _______    _______    __________

      (Intercept)     10.035     0.55554     18.064    2.2246e-08
      x1             -2.3583     0.18476    -12.765     4.542e-07

Number of observations: 11, Error degrees of freedom: 9
Root Mean Squared Error: 0.315
R-squared: 0.948,  Adjusted R-Squared 0.942
F-statistic vs. constant model: 163, p-value = 4.54e-07
>> coefCI(ci)

ans =

      8.7784   11.2919
     -2.7763   -1.9404

An I am having trouble interpreting the confidence intervals, can someone help me out please? Thanks a lot!

Answer 1

[Star Strider]

The confidence intervals correspond to:

        (Intercept)     10.035   8.7784   11.2919
        x1             -2.3583  -2.7763   -1.9404

The hypothesis the parameter confidence intervals test is that the parameters are not significantly different from zero. If they are (the confidence intervals have opposite signs) the parameter is not needed in the model. Here they both have the same signs for each parameter, so the parameters are each significantly different from zero, and both parameters are necessary to explain the model.