Question

In: Statistics and Probability

LETTER FROM THE BOSS

From: Pat Turner
Sent: Thursday, July 7, 2016 8:57 a.m.
Subject: Mystery Data Shopper Stats and Store Performance?

Good morning! Welcome back from vacation J I hope you had a wonderful Fourth of July.

The last mystery shopper surveys came in and I have the final numbers. I am interested in whether there is a way to predict the final average based on the initial survey score. Also, is there a statistically significant relationship between how stores initially performed and what the overall average is?

The initial survey score and the final average data for all seven store locations is in the table below:

Store	1	2	3	4	5	6	7
Initial Survey Score	83	97	84	72	85	64	93
Final Average	78	98	92	75	88	70	93

Also, how good is the relationship between Initial Survey Score and the Final Average? Could I use an Initial Survey Score to predict a Final Average? In fact, could I predict a Final Average if I have an Initial Survey Score of 90?

If you could have this to me before the weekend, that would be great.

Thanks so much!

Pat Turner, Owner

Chic Sales Consignment, LLC

Expert Solution

Ans:

Store	Intial(x)	Final(y)	xy	x^2	y^2
1	83	78	6474	6889	6084
2	97	98	9506	9409	9604
3	84	92	7728	7056	8464
4	72	75	5400	5184	5625
5	85	88	7480	7225	7744
6	64	70	4480	4096	4900
7	93	93	8649	8649	8649
Total=	578	594	49717	48508	51070

slope,b=(7*49717-578*594)/(7*48508-578^2)=0.8565

intercept,a=(594-0.85654*578)/7=14.131

Regression eqn:

Perdicted final score=0.8565*intial score+14.131

Correlation cofficient,r=(7*49717-578*594)/SQRT((7*48508-578^2)*(7*51070-594^2))=0.929

There is strong positive correlation between intial and final scores

cofficient of determination,r^2=0.929^2=0.863,which indicates that 86.3% of the linear variation in final score is explained by the intial score.

orchestra answered 2 years ago

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