Question

After watching the Superbowl, Steve is convinced that the referees are often blind, blowing calls that greatly influence teams’ chances of winning. To test his idea, Steve chooses ten NFL teams at random and watches every single game in a season for those ten teams. He records the number of blown calls going against each team (regardless of whether he is a fan of the team!). He also records the winning percentages of each of those ten teams at the end of the season. He is most interested in knowing whether the number of blown calls going against each team predicts those teams’ winning percentages. Using Steve’s dataset below, provide your hand calculations to answer the questions that follow.

	Blown Calls (X)	Winning Percentage (Y)	X2	Y2	XY
	50	78	2500	6084	3900
	61	83	3721	6889	5063
	66	55	4356	3025	3630
	69	73	4761	5329	5037
	73	49	5329	2401	3577
	74	59	5476	3481	4366
	79	39	6241	1521	3081
	80	45	6400	2025	3600
	85	47	7225	2209	3995
	110	32	12100	1024	3520
Total	747	560	58109	33998	39769

Steve’s favorite team had only 60 blown calls against them this season. What would you predict Steve’s team’s winning percentage to be?

Answer 1

	Blown Calls (X)	Winning Percentage (Y)	X2	Y2	XY
	50	78	2500	6084	3900
	61	83	3721	6889	5063
	66	55	4356	3025	3630
	69	73	4761	5329	5037
	73	49	5329	2401	3577
	74	59	5476	3481	4366
	79	39	6241	1521	3081
	80	45	6400	2025	3600
	85	47	7225	2209	3995
	110	32	12100	1024	3520
Total	747	560	58109	33998	39769

using this data

we can calculate the regression intercept (a) and then on the basis of that we can it to find y for a certain value of x

Now we calculate the slope

Now for calculating y we calculate b

Now we calculate y by using the formula

Y=mX+b

Y= (0.454) ( 60) + (22.087)

Y= 27.24+22.087

Y= 49.327

Hence3, the winning percentage against 60 blown calls can be predicted to be 49.327