Name: Tae Eon Kim (u0889103)
OIS – 3440 Applications of Business Statistics
Instructor: Professor Tariq Mughal
Case 15.1 Dynamic Scales
Jennie Garcia is store manager of coffee shop. She is in charge of operation and planning for the company’s southern region. And she tracks store revenue and anticipates coffee demand. As the company grew, stores become various. There are many different types of coffee shop now. So she want to figure out why there are revenue differences in stores.
The scatter plot of coffee shop is shown below.
Here x axis represents store size which is my Independent variable. And y axis represents weekly sales which is dependent variable. An upward trend is observed for store size (X) and weekly sales (Y) which ...view middle of the document...
Observations | 53 |
ANOVA | | | | | |
| df | SS | MS | F | Significance F |
Regression | 1 | 7477596 | 7477596 | 97.37338 | 2.03E-13 |
Residual | 51 | 3916444 | 76793.02 | | |
Total | 52 | 11394040 | | | |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% |
Intercept | 1612.467 | 294.3407 | 5.478232 | 1.33E-06 | 1021.553 | 2203.38 | 1021.553 | 2203.38 |
Store Size (Sq. Ft.) | 3.110897 | 0.315258 | 9.867795 | 2.03E-13 | 2.477991 | 3.743803 | 2.477991 | 3.743803 |
R12 = 0.6562 implies that 65.62% of the variation of weekly sales (Y) around its mean (y-bar) is explained by the independent variables Price for store size (X). Thus, the fitted line is a good fit to the data and the model seems to be accurate.
Regression Equation: Y = 1612.467 + 3.110897 (X)
Intercept = 1612.467, which tells me the initial value of Weekly sales (Y) when store size (X) is zero. Slope = 3.11 which tells the us that there is 3.11 units increase in weekly sales (Y) when there is unit increase in store size (X).
Ho1: β1=0, β1 is not significant
v/s H11: β1≠0, β1 is significant.
p-value = 0.0000
Since p-value < 0.05, reject H01 at 5% level of significance and conclude that β1 is significant.
Thus, Store Size (X) should be included in the model.
From the data analysis, y = 1612.467 + 3.1109 x . Weekly store sales are expected to average $5 per square foot. 1000 square foot store have average weekly sales of 5000. From this equation if x = 1000, y = 4723.367. Even there is difference between expected value and observed value. I think it is reasonable.
* There is strong linear positive relationship between store size and weekly sales.
* Large store size causes high weekly sales.
* Even there are differences between observed sales and expected sales, it is acceptable.