Question

11. For the National Football League, rating for the all-time leading passers were as shown below. Also shown for each quarterback is the percentage of passes that were interceptions, along with the percentage of passes that were touchdowns. (10 points) a) percentage of passes that were touchdowns b) Determine the standard error of estimate. TD% 5.6 5,7 5.1 5.4 Inter% 2.6 2.8 3.4 2.4 Rating 96.8 Player #1 #2 #3 #4 #5 #6 #7 | 947 93.2 92.9 92.3 90.1 89.9 5.1 4.9 3.1 3.2

Answer 1

a.

Line of Regression Y on X i.e Y = bo + b1 X

estimating the passer rating based on the percentages of [asses that were touchdowns.

here value of touch downs are dependent variables and the rating will be indendent variable.

X	Y	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
5.6	96.8	0.09878	15.65864	1.24372
5.7	94.7	0.17164	3.44882	0.7694
5.1	93.2	0.03448	0.12752	-0.06631
5.4	92.9	0.01306	0.00326	0.00653
5.2	92.3	0.00734	0.29474	0.04653
5.1	90.1	0.03448	7.5235	0.50936
4.9	89.9	0.14876	8.66066	1.13508

calculation procedure for regression

mean of X = ∑ X / n = 5.2857

mean of Y = ∑ Y / n = 92.8429

∑ (Xi - Mean)^2 = 0.50854

∑ (Yi - Mean)^2 = 35.72

∑ (Xi-Mean)*(Yi-Mean) = 3.64431

b1 = ∑ (Xi-Mean)*(Yi-Mean) / ∑ (Xi - Mean)^2

= 3.64431 / 0.50854

= 7.16622

bo = ∑ Y / n - b1 * ∑ X / n

bo = 92.8429 - 7.16622*5.2857 = 54.96441

value of regression equation is, Y = bo + b1 X

Y'=54.96441+7.16622* X

the regression equation to estimate the rating value based on the given touch down values will be,

Y'=54.96441+7.16622* X

b.

Xi	Yi	Y'=54.96+7.17*X	Y-Y'	(Y-Yi)^2
5.6	96.8	95.095	1.705	2.907
5.7	94.7	95.812	-1.112	1.237
5.1	93.2	91.512	1.688	2.849
5.4	92.9	93.662	-0.762	0.581
5.2	92.3	92.229	0.071	0.005
5.1	90.1	91.512	-1.412	1.994
4.9	89.9	90.079	-0.179	0.032

Standard error = Sqrt( ( ∑ Y -Yi )^2/ n-2 )

∑ Y -Yi )^2 = 9.605

Standard Error = 1.386

Standard Error^2 = 1.6745