Silver Screen Inc. is a movie distribution company. It has...

Silver Screen Inc. is a movie distribution company. It has kept records of total annual movie ticket sales for one community over ten years. These data have been related to other publicly available data as shown in Table 3.8. For these data: (a) Plot the data so that you can advise Silver Screen's management on a predictive model for movie ticket sales for the next few years. (b) Discuss the relative merits of various regression and smoothing models with reference to the available data. (c) Calculate both simple and multiple regressions. $$ \begin{array}{llll} \hline \hline \text { Year } & \text { Ticket sales } & \text { Households } & \begin{array}{l} \text { Average household } \\ \text { income (\$/year) } \end{array} \\ \hline 1992 & 75,000 & 20,000 & 32,250 \\ 1993 & 82,000 & 20,850 & 34,825 \\ 1994 & 81,100 & 22,000 & 37,580 \\ 1995 & 85,250 & 21,800 & 42,015 \\ 1996 & 94,350 & 21,450 & 41,870 \\ 1997 & 92,700 & 22,100 & 44,280 \\ 1998 & 95,280 & 23,750 & 47,850 \\ 1999 & 96,480 & 24,100 & 49,250 \\ 2000 & 94,300 & 24,800 & 51,380 \\ 2001 & 97,800 & 25,370 & 54,890 \\ \hline \hline \end{array} $$ (d) Calculate moving average, weighted moving average and exponential smoothing models. (e) Establish three-year forecasts under each of the above models. (f) Advise management as to the suitability and reliability of forecasts established under each model.

Silver Screen Inc. is a movie distribution company. It has kept records of total annual movie ticket sales for one community over ten years. These data have been related to other publicly available data as shown in Table 3.8.
For these data:
(a) Plot the data so that you can advise Silver Screen's management on a predictive model for movie ticket sales for the next few years.
(b) Discuss the relative merits of various regression and smoothing models with reference to the available data.
(c) Calculate both simple and multiple regressions.
$$
\begin{array}{llll}
\hline \hline \text { Year } & \text { Ticket sales } & \text { Households } & \begin{array}{l}
\text { Average household } \\
\text { income (\$/year) }
\end{array} \\
\hline 1992 & 75,000 & 20,000 & 32,250 \\
1993 & 82,000 & 20,850 & 34,825 \\
1994 & 81,100 & 22,000 & 37,580 \\
1995 & 85,250 & 21,800 & 42,015 \\
1996 & 94,350 & 21,450 & 41,870 \\
1997 & 92,700 & 22,100 & 44,280 \\
1998 & 95,280 & 23,750 & 47,850 \\
1999 & 96,480 & 24,100 & 49,250 \\
2000 & 94,300 & 24,800 & 51,380 \\
2001 & 97,800 & 25,370 & 54,890 \\
\hline \hline
\end{array}
$$
(d) Calculate moving average, weighted moving average and exponential smoothing models.
(e) Establish three-year forecasts under each of the above models.
(f) Advise management as to the suitability and reliability of forecasts established under each model.

Key Concepts

Model Evaluation

Model evaluation assesses the reliability and suitability of different predictive models by comparing their performance in explaining past data and forecasting future outcomes. This includes analyzing goodness-of-fit, error metrics, and the robustness of assumptions underlying each model.

Exponential Smoothing

Exponential smoothing is a forecasting method that applies decreasing weights to past observations, with the most recent data receiving the highest weight. It is effective in capturing trends and seasonality in time series data while being responsive to changes.

Weighted Moving Average

The weighted moving average is an extension of the simple moving average that assigns different weights to data points, typically giving more importance to the most recent observations. This technique is particularly useful when recent data is more indicative of future trends.

Moving Average

The moving average technique is a smoothing method used to reduce short-term fluctuations and highlight longer-term trends in time series data. By averaging subsets of data points, it simplifies variability and makes it easier to forecast future values.

Forecasting

Forecasting involves the use of statistical models and historical data to predict future values. It is an essential element in planning and decision-making, allowing organizations to allocate resources and strategize based on anticipated trends.

Simple Regression

Simple regression is a form of regression analysis where the relationship between a single independent variable and a dependent variable is modeled. It provides insights into how changes in one predictor are associated with changes in the response, forming the foundation for more complex predictive models.

Regression Analysis

Regression analysis is a statistical technique used to model and analyze the relationships between a dependent variable and one or more independent variables. It is useful for predicting outcomes based on input variables and for understanding the strength and nature of the associations among them.

Data Visualization

Data visualization involves plotting data to reveal patterns, trends, and anomalies. It is crucial for understanding underlying structures in the data, such as trends over time, seasonal effects, or sudden changes, and serves as a preliminary step before applying more formal analytical techniques.

Multiple Regression

Multiple regression extends the simple regression model by incorporating two or more independent variables to explain the variability in a dependent variable. This approach accounts for the combined effect of several predictors and is useful for capturing more complex relationships in the data.

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