<p>Unfortunately not, as in frequentist statistics the true slope is not a random variable.  This leads to a bit of a mouthful as the conclusion</p>

<p>What you could say is that if your assumptions are correct (such as a linear relationship with random errors) and you repeated the exercise with new sample data and new regressions, $95\%$ of the confidence intervals you would generate for the slope would contain the true value</p>

<p>So you have one interval from a procedure which generates correct intervals $95\%$ of the time </p>

CC BY-SA 3.0
2017-01-16T07:53:30.923Z
2017-01-16T07:53:30.923Z
Henry
<p>In R I have used <code>lm()</code>to fit a model. Then I use the <code>confint()</code> function to learn more about the slope. How to I understand the following result? Is the following conclusion true:</p>

<p><strong>With 95% probability the slope is between 1232.44 and 1259.912?</strong></p>

<pre><code>&gt; confint(fit1)
              2.5 %    97.5 %
(Intercept) 14161.38 14649.096
car.sales     1232.44  1259.912
</code></pre>

CC BY-SA 3.0
2017-01-16T09:36:50.147Z
You may find it helpful to look at Cross Validated SE where there has been extensive discussion of the interpretation of confidence intervals, eg here (http://stats.stackexchange.com/questions/26450/why-does-a-95-confidence-interval-ci-not-imply-a-95-chance-of-containing-the)
Adam Bailey
CC BY-SA 3.0
2017-01-16T10:26:42.903Z
I'm voting to close this question as off-topic because this is a basic statistics question with no economics content.
BKay
<statistics><regression><r>
Statistics: Understanding confidence interval
Rakesh
# Statistics: Understanding confidence interval

(Asked by: username_0 on 2017-01-15)

In R I have used `lm()`to fit a model. Then I use the `confint()` function to learn more about the slope. How to I understand the following result? Is the following conclusion true:

**With 95% probability the slope is between 1232.44 and 1259.912?**

```
> confint(fit1)
              2.5 %    97.5 %
(Intercept) 14161.38 14649.096
car.sales     1232.44  1259.912

```

**Tags:** statistics, regression, r

> **Comments:**
> **username_1**: You may find it helpful to look at Cross Validated SE where there has been extensive discussion of the interpretation of confidence intervals, eg here (http://stats.stackexchange.com/questions/26450/why-does-a-95-confidence-interval-ci-not-imply-a-95-chance-of-containing-the)  
> **username_2**: I'm voting to close this question as off-topic because this is a basic statistics question with no economics content.  

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## 1 answers

### Answer by username_3 on 2017-01-16. Score: 1

Unfortunately not, as in frequentist statistics the true slope is not a random variable. This leads to a bit of a mouthful as the conclusion

What you could say is that if your assumptions are correct (such as a linear relationship with random errors) and you repeated the exercise with new sample data and new regressions, $95\%$ of the confidence intervals you would generate for the slope would contain the true value

So you have one interval from a procedure which generates correct intervals $95\%$ of the time


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