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I have computed some regression data for the two variables I am investigating, I am trying to prove there is a positive relationship between the 2 variables. My first question is why is it that only the data for the independent variable is shown; what about the dependent variable?

My second question is why is the data 'Lower 95%' and 'Upper 95%' repeated twice?

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  • $\begingroup$ You've got good advice. If you need more, show us the data. Regardless of that, you appear to be puzzled about the results, and plotting the data are the best way to understand them. $\endgroup$
    – Nick Cox
    Apr 18, 2018 at 12:43

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The regression you are doing aims to show the effect of the independent variable on the dependent variable. Your dependent variable "depends" on the independent variable, and it shouldn't make sense to test the opposite effect. For example, imagine your dependent variable was plant growth, and your independent variable was hours of sunshine per day. It makes sense to test for an effect of the hours of sunshine on crop growth. However, it would make no sense to test the opposite effect - crop growth couldn't possibly have an effect on the amount of sunshine. If your two variables are completely unrelated you might be better doing a correlation rather than a regression.

I'm not sure why Excel shows the 95% upper and lower bounds twice. If you had chosen a different confidence interval earlier (e.g. 99%) when specifying the model, it would display the 95% and 99% intervals instead of showing 95% twice.

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  • $\begingroup$ Thank you for the reply. I have just run my regression again and noticed that now both my upper and lower confidence intervals are negative. What can I deduce from this information? Isn't the higher the confidence interval, the stronger the relationship ? Does this mean a negative relationship is shown? $\endgroup$
    – rainbow21
    Apr 18, 2018 at 12:13
  • $\begingroup$ If your upper and lower confidence intervals are both negative, this suggests a significant effect of the independent variable on the dependent variable - is your p-value below 0.05? Look at the coefficient to see the direction of the effect - a negative value would indicate a negative relationship. $\endgroup$
    – rw2
    Apr 18, 2018 at 12:56
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Peter Flom’s answer as above is on-point. On your follow up, the confidence interval (CI) gives you two important pieces of information: the estimate of effect and the precision of your estimate.

1) Effect estimate: Your CI has a lower bound of -1.356 and an upper bound of 0.234. A negative number indicates a negative relationship and a positive one indicates a positive one. Note that your CI includes the value 0, which would suggest no relationship.

2) Precision: how “wide” your estimate is, i.e. The distance between upper and lower bounds. If the distance is small or narrow, the estimate is quite precise. A wide estimate including 0 such as yours suggest the data are very scattered, and we can’t get enough information from your sample to indicate that a true relationship exists.

A clue to interpretation exists in the p-value. When we run the statistical test on your data, we are calculating the likelihood we would see the pattern shown by your exact data in “infinite” imaginary samples if there were truly no association between the dependent and independent variables.

Unfortunately your p-value is fairly high, and together with your confidence interval suggest that there is no evidence for a relationship when just comparing these two variables with your data. If anything, there is (very very weak) evidence suggesting there could be a negative relationship, but really we don’t know.

A CI and p-value go hand-in-hand. The narrower a CI and the farther it is from 0, the lower the p-value.

Your intercept tests give a very different set of stats, but unfortunately in a linear regression this isn’t the main item of interest: the value of x1 is the key item, and if anything the data suggest your independent y variable may clustered around a certain value for reasons unrelated to the dependent variable.

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    $\begingroup$ Helpful (+1). In your last paragraph I think you mean "the value of the coefficient of x1" $\endgroup$
    – Nick Cox
    Apr 18, 2018 at 12:42
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    $\begingroup$ If @Peter Flom posted anything here, it's now disappeared. $\endgroup$
    – Nick Cox
    Apr 18, 2018 at 12:44
  • $\begingroup$ Yes, thanks for noting linguistic sloppiness wrt algebra: the coefficient of x1, ie -0.56, is the important bit of info for the OP. $\endgroup$
    – JYS
    Apr 18, 2018 at 14:55

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