To: Mrs.Turner
Sent: Wednesday, 11 April.
Subject: Mystery Data Shopper Stats and Store Performance
Regression Models Case Study: Mystery Shoppers
Predicting the final scores involved using initial count values to regression equation will be utilized. The line of best fit was established and used in coming up with the regression equation formulated and used in predicting the final scores. A hypothesis was formulated to determine the statistical significance of the data. formulatedDetermining the statistical significance, and whether a store location should be closed based on the data provided. Evaluate the outcomes of your regression model and the responses to Mrs. Turner’s questions. Research indicated customer satisfaction had decreased and the owner, Pat Turner, decided to create a mystery shopper program.
Store Initial Survey Score Final Average
1 83 78
2 97 98
3 84 92
4 72 75
5 85 88
6 64 70
7 93 93
Regression output results.
Coefficients
Intercept 14.13121345
X Variable 1 0.856542398
Prediction of the average based on the initial survey score.
The regression equation is given by:
Y = max + c
Where:
Y = Final Average
C = Initial survey score
m – Slope (change in y in respect to change in x)
c – Intercept
From the regression equation, the following can be deduced:
Final average = m(initial survey score) + c
Y = 0.857x + 14.13
Hence;
Final average = 14.131 + 0.857(Initial survey score)
Statistical significance between how stores initially performed and what the overall average.
The F-statistics was used in establishing whether the initial score values and final values are significantly different.
Hypothesis:
Null Hypothesis: the original count values and last values are not significantly different
Alternative explanation: the initial count values and final values are significantly different
F Significance F
31.39430317 0.002502171
The significance F is 0.0025 while the F statistic is 31.394. Since the Fstatistic>Fcritical, we reject the null hypothesis that says that the initial score values and final values are not significantly different. Instead, the alternative we accept the alternative hypothesis that states that the original score values and last values are significantly different and therefore conclude that the initial scores and final values are significantly different meaning that they were drawn from different populations and thus the ratings are not biased.
The p-value.
P-value
Intercept 0.317333338
X variable 1 0.002502171
The p-value is 0.3173 for the intercept while that of the x variable is 0.0025. Since the p-value of the x variable is are less than the level of significance which is 0.05, it is, therefore, conclusive to say that there is a significant relationship between how stores initially performed and their final scores.
How good is the relationship between Initial Survey Score and the Final Average?
The correlation results are used to establish the connection between the Initial survey score and the final average. The relationship between the original review score and the final average is 0.9288. Essentially, it is evident to see that there is a strong correlation between the two values since it is closer to 1. Thus, the initial survey score and the final average had a strong positive correlation between one another.
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?
The coefficient of determination establishes the extent to which the dependent variable is predictable. A coefficient of determination of (r2) of 0.8626 means that 86.26percent of the variance in the final average is predictable from the Initial survey score.
The final average of an initial survey score of 90 is given by:
Final average = 14.131 + 0.857(Initial survey score)
Final average = 14.131 + 0.857*90
Final average = 14.131 + 77.13
Final average = 91.261.