Question

State Debt and Per Capita Tax Data for per capita state debt and per capita state tax for nine randomly selected states are shown. The correlation coefficient is

=r0.420

. Compute the standard error of the estimate rounded to at least two decimal places, if appropriate. Assume

=α0.05

.

Per capita debt x	3691	1727	2230	1229	661	1913	1455	907	2176
Per capita tax y	2069	2179	2324	2158	1434	2049	1948	2054	1910

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	15989	18125	6455144.222	501482.9	755533.56
mean	1776.56	2013.89	SSxx	SSyy	SSxy

sample size ,   n =   9          
here, x̅ = Σx / n=   1776.56   ,     ȳ = Σy/n =   2013.89  
                  
SSxx =    Σ(x-x̅)² =    6455144.2222          
SSxy=   Σ(x-x̅)(y-ȳ) =   755533.6          
                  
estimated slope , ß1 = SSxy/SSxx =   755533.6   /   6455144.222   =   0.1170
                  
intercept,   ß0 = y̅-ß1* x̄ =   1805.9544          
                  
so, regression line is   Ŷ =   1805.9544   +   0.1170   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    413052.494          
                  
std error ,Se =    √(SSE/(n-2)) =    242.92

Thanks in advance!

revert back for doubt

Please upvote