Question

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

Completion Percentage	59	59	59	60	61
Interception Percentage	4.5	3.9	3.4	2.1	2

Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0=67.2500 and b1=−1.0750 for the calculations. Round your answer to three decimal places.

Step 2 of 5: Calculate the estimated variance of errors, s2e. Round your answer to three decimal places

Step 3 of 5: Calculate the estimated variance of slope, s2b1. 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.(Lower Endpoint, Upper Endpoint)

Step 5 of 5: Construct the 90% confidence interval for the slope. Round your answers to three decimal places.(Lower Endpoint, Upper Endpoint)

Answer 1

Step 1: From the given data

	X	Y	X^2	Y^2	XY
	59	4.5	3481	20.25	265.5
	59	3.9	3481	15.21	230.1
	59	3.4	3481	11.56	200.6
	60	2.1	3600	4.41	126
	61	2	3721	4	122
Total:	298	15.9	17764	55.43	944.2

and we predict the value y (i.e.y-hat) from the regression equation

X	Y	Ycap/fit	(Y-Ycap)^2	(Y-Ybar)^2	(Ycap-Ybar)^2
59	4.5	3.8250	0.4556	1.7424	0.4160
59	3.9	3.8250	0.0056	0.5184	0.4160
59	3.4	3.8250	0.1806	0.0484	0.4160
60	2.1	2.7500	0.4225	1.1664	0.1849
61	2	1.6750	0.1056	1.3924	2.2650
298	15.9		1.1700	4.8680	3.6980

From the above table, SSE = 1.170

Step 2: S_e² = MSE = SSE / n-2 = 1.170 / (5-2) = 0.39