Statistical Analysis Assignment: Forecasting and Regression Models

This assignment presents a statistical analysis solution addressing forecasting and regression techniques. It begins with the calculation of Mean Absolute Deviation (MAD) and Mean Squared Error (MSE) for car sales data. The assignment then explores moving average and weighted moving average forecasting methods, including the calculation of forecasts for year 13 and MAD values for each method. A comparison of the two forecasting methods is provided, with a recommendation based on the MAD values. Furthermore, the document analyzes linear and polynomial regression models, determining the R-squared values and regression formulas for each. The polynomial model is recommended based on its higher R-squared value. The document includes detailed work, charts, and references to support the findings. The case study focuses on Colonial Broadcasting Company, requiring analysis of factors driving movie ratings, alongside forecasting and regression analysis.

Running head: STATISTICAL ANALYSIS 1
Statistical Analysis
Student Name
Professor’s Name
University Name
Date

STATISTICAL ANALYSIS 2
Statistical Analysis
Assessment Answers by (Insert your name here)
This template is only for the first part of the assignment. See specific instructions in the
Assessment for Part 2.
In the summary tables below, insert only the answers. You will show work after the summary
section.
Question 1
MAD 12.50
MSE 191.90
Question 2
a) Moving average forecast for year 13 3244.34
b) Weighted moving average forecast for year 13 3384.26
c) MAD for part a 588.19
d) MAD for part b 565.28
e) Recommended forecast method (justify): The weighted moving average is the
most recommended forecast method
because it has less MAD.
Question 3
R-squared for Linear model 0.9468
R-squared for polynomial model 0.9796
Regression formula for linear model Y =10860 x +24413
Where Y is the total number of new orders
and x is the year.

STATISTICAL ANALYSIS 3
Regression formula for polynomial model Y =374.6 x2 +2618.9 x+56004
Where Y is the total number of new orders
and x is the year.
Recommended forecast method (justify): The polynomial method is more
recommended than the linear method
because it has a higher R-squared value
which means that more variability of the
variables would be explained by the fitted
model (Bruce, 2015).
Work
Show all your work for the questions below.
Question 1
The formula for error is:
Error=Value−Forecast

STATISTICAL ANALYSIS 4
The Mean Absolute deviation is given by:
MAD= ∑ |Value −Forecast |
n
The mean squared error is given by:
MSE=∑ |Value−forecast|2
n
Question 2
The table showing the forecasts and the errors is shown below.
NB: Year 13 of the data is empty so the assumption is that there were zero factory orders during
this year.
All computations are done in excel.
Year Factory Orders 5 year Moving Average Weights 5 year weighted average Moving average error ABS|Error| Weighted Average Error ABS[ERR0R]
1 2512.70 1
2 2739.20 1
3 2874.90 2
4 2934.10 4
5 2865.70 6
6 2978.50 2785.32 2852.31 193.18 193.18 126.19 126.19
7 3092.40 2878.48 2915.44 213.92 213.92 176.96 176.96
8 3052.60 2949.12 3000.63 103.48 103.48 51.97 51.97
9 3145.20 2984.66 3031.57 160.54 160.54 113.63 113.63
10 3114.10 3026.88 3079.33 87.22 87.22 34.77 34.77
11 3257.40 3076.56 3102.96 180.84 180.84 154.44 154.44
12 3654.00 3132.34 3174.01 521.66 521.66 479.99 479.99
13 0.00 3244.66 3384.26 -3244.66 3244.66 -3384.26 3384.26
MAD 588.19 565.28

STATISTICAL ANALYSIS 5
Question 3
The linear trendline chart from the Excel charting is illustrated below:
The equation is:
Y =10860 x +24413
Where Y is the total number of new orders and x is the year (Croucher, 2016). The R-squared is
0.9468
The polynomial trendline chart from excel charting is illustrated below.
.
The equation is:
Y =374.6 x2 +2618.9 x+56004
Where Y is the total number of new orders and x is the year. The R-squared is 0.9796

STATISTICAL ANALYSIS 6
References
Bruce, P. (2015). Introductory statistics and analytics. New Jersey: Wiley.
Croucher, J. S. (2016). Introductory mathematics & statistics (6th ed). Australia: North Ryde,
N.S.W. McGraw-Hill Education.
.