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, $\beta_1$ 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 $\alpha=5$% level of significance."
But it is not understandable to those who don't know statistics.
How can i interpret it more generally?