Question

The data from exercise 3 follow.

xi	2	6	9	13	20
yi	7	18	9	26	23

The estimated regression equation is ŷ = 7.6 + .9x.

1. What is the value of the standard error of the estimate (to 4 decimals)?
   
2. What is the value of the t test statistic (to 2 decimals)?
   
   
   What is the p-value?
   - Select your answer -less than .01between .01 and .02between .02 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 3
   
   What is your conclusion (α = .05)?
   - Select your answer -Conclude a significant relationship exists between x and yCannot conclude a significant relationship exists between x and yItem 4
3. Use the F test to test for a significant relationship. Use α = .05.
   
   Compute the value of the F test statistic (to 2 decimals).
   
   
   What is the p-value?
   - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6
   
   What is your conclusion?

Answer 1

.

What is the value of the standard error of the estimate (to 4 decimals)

sample size ,   n =   5          
here, x̅ = Σx / n=   10.00   ,     ȳ = Σy/n =   16.60  
                  
SSxx =    Σ(x-x̅)² =    190.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   171.0          
                  
estimated slope , ß1 = SSxy/SSxx =   171.0   /   190.000   =   0.9000
                  
intercept,   ß0 = y̅-ß1* x̄ =   7.6000          
                  
so, regression line is   Ŷ =   7.6000   +   0.9000   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    127.300          
                  
std error ,Se =    √(SSE/(n-2)) =    6.5141

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What is the value of the t test statistic (to 2 decimals)?

Ho:   ß1=   0          
H1:   ß1╪   0          
n=   5              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    6.514   /√   190.00   =   0.4726
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    0.9000   /   0.4726   =   1.90

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Degree of freedom ,df = n-2=   3              
p-value =    0.1530              


What is the p-value?
between .10 and .20

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What is your conclusion (α = .05)?
Cannot conclude a significant relationship exists between x and y

1. Use the F test to test for a significant relationship. Use α = .05.
   
   Compute the value of the F test statistic (to 2 decimals).

   Anova table
   variation	SS	df	MS	F-stat	p-value
   regression	153.900	1	153.900	3.63	0.1530
   error,	127.300	3	42.433
   total	281.200	4

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greater than .10

Cannot conclude a significant relationship exists between x and y

thanks

revert back for doubt

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