Interpreting confidence interval of regression coefficient.In a Simple Linear Regression analysis, independent variable is weekly income and dependent variable is weekly consumption expenditure.Here 95% confidence interval of regression coefficient, β 1 is (.4268,.5914).So i have interpreted as :"The data provides much evidence to conclude that the true slope of the regression line lies between .4268 and .5914 at α = 5% level of significance."But it is not understandable to those who don't know statistics.How can i interpret it more generally?

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Interpreting confidence interval of regression coefficient.In a Simple Linear Regression analysis, independent variable is weekly income and dependent variable is weekly consumption expenditure.Here 95% confidence interval of regression coefficient,       β    1   is (.4268,.5914).So i have interpreted as :&quot;The data provides much evidence to conclude that the true slope of the regression line lies between .4268 and .5914 at   α  =  5% level of significance.&quot;But it is not understandable to those who don&#039;t know statistics.How can i interpret it more generally?

fongama33 · Accepted Answer

First in statistical speak:Our model is       Y    i    =      β    0    +      β    1        X    i    +      ε    i  . This means that       β    1   is the amount that we expect Y to increase by when X increases by 1 [or decrease if       β    1    &amp;lt;  0].Now in terms of the problem:In this problem X is weekly income and Y is weekly consumption expenditure so                     β        1            ^       is our estimate of the amount that weekly consumption expenditure increases for every $1 increase in weekly income. We are 95% confidence that it is between 0.43 and 0.59 [where by &quot;95%&quot; confidence we mean that if we were to collect new data generated from the same distribution then in 19 out of every 20 experiments we&#039;d get                     β        1            ^       in this interval].

Interpreting confidence interval of regression coefficient. In a Simple Linear Regression analysis,

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