Question

For Problems 1 and 3, do a complete regression analysis by performing the following steps:

1. Draw the scatter plot.

2. Compute the value of the correlation coefficient.

3. Test the significance of the correlation coefficient at α = 0.01.

4. Determine the regression line equation if r is significant.  

5. Plot the regression line on the scatter plot if appropriate.

6. Predict y’ for a specific value of x if appropriate.  

I need an answer on question 2 (bold)

1. Listed below are the number of touchdown passes thrown in the season and the quarterback rating for a random sample of NFL quarterbacks. Is there a significant linear relationship between the variables?

2. For Problem 1, find the standard error of the estimate.

TDs	34	21	15	22	34	26	23
QB rating	106	89	82	81	96	91	86

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	175	631	292	454.9	318.00
mean	25.00	90.14	SSxx	SSyy	SSxy

Determine the regression line equation if r is significant.

sample size ,   n =   7          
here, x̅ = Σx / n=   25.00   ,     ȳ = Σy/n =   90.14  
                  
SSxx =    Σ(x-x̅)² =    292.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   318.0          
                  
estimated slope , ß1 = SSxy/SSxx =   318.0   /   292.000   =   1.0890
                  
intercept,   ß0 = y̅-ß1* x̄ =   62.9168          
                  
so, regression line is   Ŷ =   62.9168   +   1.0890   *x

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Compute the value of the correlation coefficient.

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    108.542          
                  
std error ,Se =    √(SSE/(n-2)) =    4.6592          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.8726          

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Test the significance of the correlation coefficient at α = 0.01

Ho:   ρ = 0       tail=   2  
Ha:   ρ ╪ 0              
n=   7              
alpha,α =    0.01   
correlation , r=   0.8726              
t-test statistic = r*√(n-2)/√(1-r²) =        3.994          
DF=n-2 =   5              
p-value =    0.0104              
Decison:   p value > α , So, Do not Reject Ho         

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2. For Problem 1, find the standard error of the estimate.

std error ,Se =    √(SSE/(n-2)) =    4.6592
   

thanks

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