A computer chip is a critical component composed of micro$-$sized transistors that act as tiny

switches, controlling the flow of electrons. Despite their small size $($no larger than a human

fingernail$),$ these chips play a crucial role in various industries, including appliances, airplanes,

machine tools, healthcare equipment, transportation, smartphones, and electronic payment

systems.

Due to the combined demand from multiple industries and the disruptions caused by the COVID$-$

$19$ pandemic, there is a global shortage of computer chips. Factors contributing to this shortage

include limited worldwide factory capacity, trade wars, hoarding, production shutdowns, shipping

and seaport bottlenecks, and other supply chain issues. Building new chip factories to increase

production capacity takes several years, and even after completion, it takes additional months to

ramp up production. Additionally, lead times for new chip orders range from six months to a year.

The average electric vehicle relies on approximately $2,000$ computer chips, responsible for

controlling and monitoring various functions such as fuel consumption, braking, airbags, driver

assistance, music channels, navigation, communications, and electronic displays. Here we focus

on a specific chip, PVENT$902,$ which is used in vehicle airbags. The following data represents

quarterly sales demand for this chip in $100,000$ units over the past five years. While there is an

overall increasing trend in sales, the time series pattern suggests that the demand is influenced by

the quarter of the year. The objective is to forecast the future demand for this chip.

Time Series Year Quarter Sales$*$

$1114$

$2129$

$3138$

$41411$

$52111$

$6229$

$72313$

$82415$

$93114$

$103212$

$113317$

$123416$

$134116$

$144219$

$154322$

$164423$

$175120$

$185225$

$195328$

$205431$

$*$times $[100,000]$

a$)$ Determine the best moving average and best simple exponential smoothing model that

can be used to forecast the future demand for the PVENT$902$ chip. Assess the models

using the Mean Squared Error $($MSE$)$ evaluation metric. $(8$ marks$)$

$($Hint: Try a range of values for the number of periods and smoothing constant to

determine the best models$)$

b$)$ Compare the performance of a simple linear trendline forecast with the best moving

average and exponential smoothing models using the Mean Squared Error $($MSE$)$ metric.

$(3$ marks$)$

c$)$ As the sales of the chip appear to be influenced by the quarter of the year, develop a

multiple regression model to forecast the sales and compute the MSE. How does this model

compare to the models discussed in questions $1$ and $2?($Note: if you are using Excel to

build the regression mode, you should place time series and quarter variables side by side$).$

$(5$ marks$)$

d$)$ Summarize your results and recommendations in a short memo to the company. $(3$

marks$)$