Simple Regression Models Case Study: Mystery Shoppers Chic Sales is a high-end c
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Simple Regression Models Case Study: Mystery Shoppers
Chic Sales is a high-end consignment store with several locations in the metro area. The company noticed a decrease in sales over the last fiscal year. Research indicated customer satisfaction had decreased and the owner, Pat Turner, decided to create a mystery shopper program.
The mystery shopper program lasted over a 6-month period, employing several loyal and new customers assigned to each location. Surveys were on a 100-point scale and involved categories such as “Staff Attitude,” “Store Cleanliness,” “Product Availability,” and “Display(s) Appeal.”
After the mystery shopper period concludes, Mrs. Turner sends you the following e-mail:
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
I need help answering these questions because I have already done the linear regression on excel and this is what i came up with. (91.22)
With these numbers I need help understanding if a store location should be closed based on the data?
Is there a way to predict final average based on the initial survey?
If there is a significant relationship between how stores initially performed and what the over all average is?
How good is the initial score and the final average? Can I predict a final average if i have an initial score of 90?
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
Explanation / Answer
Consider the null hypothesis, ho: there a no statistically significant relationship between how stores initially performed and what the overall average is. Versus alternative hypothesis, h1:there a statistically significant relationship between how stores initially performed and what the overall average is.
From the ANOVA table in the regression output, F=31.39 and p-value = 0.0025. With F=31.39 and p-value less than alpha (0.05), I reject ho at 5% level of significance and conclude that there a statistically significant relationship between how stores initially performed and what the overall average is.
R2= 0.8626 implies that 86.26% of the variation of Final Average (Y) around its mean (y-bar) is explained by the independent variable Initial Survey Score (X). Thus, the fitted line is a good fit to the data and the model seems to be accurate.
Regression equation is given by: Final average = 14.13 + 0.8565*Initial Survey Score
The value of intercept, 14.13, is the initial value of final average when initial survey score is zero. The significant slope, 0.8586 implies that with a unit increase in initial survey score,there is 0.8565 units increase in final average. When, Initial Survey Score is 90, then predicted Final average = 14.13 + 0.8565*90 =91.215
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