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 ).

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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  ).

luthersavage6lm · 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].

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).

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