Kayley Dickson

2022-11-18

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 $\left(.4268,.5914\right)$.

luthersavage6lm

First in statistical speak:
Our model is ${Y}_{i}={\beta }_{0}+{\beta }_{1}{X}_{i}+{\epsilon }_{i}$. This means that ${\beta }_{1}$ is the amount that we expect $Y$ to increase by when $X$ increases by $1$ [or decrease if ${\beta }_{1}<0$].
Now in terms of the problem:
In this problem $X$ is weekly income and $Y$ is weekly consumption expenditure so $\stackrel{^}{{\beta }_{1}}$ is our estimate of the amount that weekly consumption expenditure increases for every $\mathrm{}1$ increase in weekly income. We are $95$% confidence that it is between $0.43$ and $0.59$ [where by "$95$%" 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'd get $\stackrel{^}{{\beta }_{1}}$ in this interval].

Do you have a similar question?