Forecasting Restaurant Sales

Forecasting Restaurant Sales

  1. A time series plot. Comment on the underlying pattern in the time series.

A time series plot refers to a graph used in evaluating patterns and behavior in data over time, in this case it is used in evaluating food and beverage sales. The paper aims at developing a system that will enable the owner of C’mon Back Restaurant in Puerto Rico, Theotis Jones, forecast food and beverage sales by month for up to one year in advance so as to better plan for future growth of the restaurant.

The graph of the time series is as shown below.

From the time series plot, it is evident that the graphs indicate an upward trend in that the food and beverage sales increased from year one to year three. The sales in the second year are higher than those of the first year and the food and beverage sales for year three are greater than those of the second year. However, the sales of each year fluctuated across the period, it is evident that the sales for all the years decreased in April, June and September but increased in May, August and December. This implies that there is slightly significant seasonal component in the time series. The fluctuating trend implies that there is sufficient evidence to conclude that there exists significant seasonal component in the time series. However, in general, there is an upward trend in the food and beverage sales volume and this implies that the restaurant will have increased profit in the years to come. For instance, sales for the company show slow, moderately steady growth but with lesser monthly sales fluctuations.

 

  1. Using the dummy variable approach, forecast sales for January through December of the fourth year. How would you explain this model to Theotis?
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.904848
R Square 0.81875
Adjusted R Square 0.715178
Standard Error 1.924235
Observations 12
ANOVA
  df SS MS F Significance F
Regression 4 117.0812 29.27031 7.905164 0.009799
Residual 7 25.91877 3.702682
Total 11 143      
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 13.52231 2.544744 5.31382 0.001107 7.504947 19.53967 7.504947 19.53967
1st Year 0.026113 0.153267 0.170379 0.869532 -0.3363 0.388532 -0.3363 0.388532
2nd Year 0.345888 0.125423 2.757769 0.028186 0.049309 0.642466 0.049309 0.642466
3rd Year -0.39205 0.18433 -2.12688 0.070996 -0.82792 0.043823 -0.82792 0.043823
Effect dummy 3.287767 1.13989 2.884283 0.023507 0.592354 5.98318 0.592354 5.98318
Predicted sales = 13.5223 + 0.0261*Year 1 sales + 0.3459* year 2 sales -0.3921*year 3 sales +3.2878*D

 

 

Using the formula to find the forecasted sales

Month 1st Year 2nd Year 3rd Year 4th Year
1 242 263 282 296.458
2 235 238 255 274.191
3 232 247 265 280.341
4 178 193 205 216.936
5 184 193 210 221.177
6 140 149 160 169.223
7 145 157 166 176.221
8 152 161 174 183.431
9 110 122 126 134.869
10 130 130 148 153.742
11 152 167 173 185.339
12 206 230 235 252.774

 

Assume that January sales for the fourth year turn out to be $295,000. What was your forecast error? If this error is large, Theotis may be puzzled about the difference between your forecast and the actual sales value. What can you do to resolve his uncertainty about the forecasting procedure?

The actual January sales for the fourth year turned out to be $295,000 while the forecasted January sales are $296,458.

Therefore, the error between the sales = $296,458 – $295,000 = $1458

Percentage Error =

A percentage error of 0.49% is an extremely small percentage error and Theotis does not have to worry about it as he can be assured that his forecast model is extremely good.

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