Question

The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks.

Completion Percentage   Interception Percentage
55   4.3
59   2.2
61   1.9
62   1.8
66   1.7

Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0=16.4513and b1=−0.2322 for the calculations. Round your answer to three decimal places.

Step 2 of 5: Calculate the estimated variance of errors, se2. Round your answer to three decimal places.

Step 3 of 5: Calculate the estimated variance of slope, s^2b1. Round your answer to three decimal places.

Step 4 of 5: Construct the 98% confidence interval for the slope. Round your answers to three decimal places.

Step 5 of 5: Construct the 99% confidence interval for the slope. Round your answers to three decimal places.

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	303.00	11.90	65.20	4.75	-15.14
mean	60.60	2.38	SSxx	SSyy	SSxy

Sample size,   n =   5      
here, x̅ = Σx / n=   60.600          
ȳ = Σy/n =   2.380          
SSxx =    Σ(x-x̅)² =    65.2000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -15.1      
              
estimated slope , ß1 = SSxy/SSxx =   -15.14/65.2=   -0.2322      
intercept,ß0 = y̅-ß1* x̄ =   2.38- (-0.2322 )*60.6=   16.4513   
              
Regression line is, Ŷ=   16.4513 + (   -0.2322   )*x

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    1.232

.............

b)

std error ,Se =    √(SSE/(n-2)) =    0.6409
Se^2 = 0.411

...........

c)

estimated variance of slope ,    Se²(ß1) = Se²/Sxx =    0.006

....

d)

α=   0.02              
t critical value=   t α/2 =    4.541   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    0.6409/√65.2=   0.079          
                  
margin of error ,E= t*std error =    4.541   *   0.079   =   0.360419
estimated slope , ß^ =    -0.2322              
                  
lower confidence limit = estimated slope - margin of error =   -0.2322   -   0.360   =   -0.5926
upper confidence limit=estimated slope + margin of error =   -0.2322   +   0.360   =   0.1282
98% CI ( - 0.593 , 0.128)

..............

E)

α=   0.01              
t critical value=   t α/2 =    5.841   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    0.6409/√65.2=   0.079          
                  
margin of error ,E= t*std error =    5.841   *   0.079   =   0.463623
estimated slope , ß^ =    -0.2322              
                  
lower confidence limit = estimated slope - margin of error =   -0.2322   -   0.464   =   -0.6958
upper confidence limit=estimated slope + margin of error =   -0.2322   +   0.464   =   0.2314  
99 % CI ( -0.696 , 0.231)

..............

Please let me know in case of any doubt.

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