Question

The following table compares the completion percentage and interception percentage of 55 NFL quarterbacks.

Completion Percentage	57	60	62	63	64
Interception Percentage	4.7	4.4	3.5	2.5	2.4

Step 1 of 5 :  

Calculate the sum of squared errors (SSE). Use the values b0=25.3545 and b1=−0.3571 for the calculations. Round your answer to three decimal places.

Step 2 of 6: Calculate the estimated variance of errors, s²_e. Round your answer to three decimal places.

Answer =

Step 3 of 6: Calculate the estimated variance of slope, s²_b1. Round your answer to three decimal places.

Answer =

Step 4 of 6 : Construct the 90% confidence interval for the slope. Round your answers to three decimal places.

Lower endpoint??

Upper Endpoint??

Step 5 of 6 :  

Construct the 95% confidence interval for the slope. Round your answers to three decimal places.

Lower end point?

upper endpoint?

Step 6 of 6: Construct the 80% confidence interval for the slope. Round your answers to three decimal places.

Lower ?

Upper?

Answer 1

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	57	4.7	17.6400	1.4400	-5.0400
2	60	4.4	1.4400	0.8100	-1.0800
3	62	3.5	0.6400	0.0000	0.0000
4	63	2.5	3.2400	1.0000	-1.8000
5	64	2.4	7.8400	1.2100	-3.0800
Total	306	17.5	30.8000	4.4600	-11.0000
Mean	61.200	3.500	SSX	SSY	SXY

Step 1 of 5 :  

SSE =Syy-(Sxy)2/Sxx=

0.531

Step 2 of 6:

error Variance σ2 =

s2 =SSE/(n-2)

=

0.177

Step 3 of 6: Calculate the estimated variance of slope, s²_b1.=s²/SSX =0.006

Step 4 of 6 : Construct the 90% confidence interval for the slope:

for 90 % CI value of t=					2.3530
margin of error E=t*std error                            =					0.178
lower confidence bound=estimated slope-margin of error =					-0.536
Upper confidence bound=estimated slope+margin of error=					-0.179

Step 5 of 6 :  

Construct the 95% confidence interval for the slope :

lower confidence bound=estimated slope-margin of error =					-0.598
Upper confidence bound=estimated slope+margin of error=					-0.116

Step 6 of 6: Construct the 80% confidence interval for the slope:

lower confidence bound=estimated slope-margin of error =					-0.481
Upper confidence bound=estimated slope+margin of error=					-0.233