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).

Kayley Dickson

Kayley Dickson

Answered question

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, β 1 is ( .4268 , .5914 ).

Answer & Explanation

luthersavage6lm

luthersavage6lm

Beginner2022-11-19Added 22 answers

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 < 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 " 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 β 1 ^ in this interval].

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