Questions:

$1.$ Forecast demands for using weighted moving average. Please apply weights of $0\mathrm{.}3$ for most recent period, then $0\mathrm{.}4,$ then $0\mathrm{.}3$

Period Demand Forecast

$16$

$212$

$314$

$418$

$522$

$625$

$728$

$2.$ Given the following data:

Prepare a forecast using smoothing constant $=0\mathrm{.}40.$

a$)$ Subjective estimate $($for this example, use $60).$

b$)$ First actual value $($na$$ve approach$).$

Period Actual Forecast Calculations

$163$

$252$

$356$

$462$

$3.$ Given the following data:

c$)$ What are the exponential smoothing forecasts for periods $2-5$ using $=0\mathrm{.}7?$

d$)$ Use na$$ve approach for $1$st week

Week Demands

$1830$

$2765$

$3630$

$4640$

$5$

$4.$ Predict quarterly demand for a certain loveseat. The series has both trend and seasonality and the Quarterly relatives are: Q$1=1\mathrm{.}20,$ Q$2=1\mathrm{.}10,$ Q$3=0\mathrm{.}75,$ Q$4=0\mathrm{.}95.$ If the trend equation equals to yt$=124+7\mathrm{.}5$t $($t $=$ quarter $15),$ Predict demand for quarter $2($where t $15=$ quarter $2).$

$5.$ Given the following data, compute MAD, MSE, and MAPE for the following data. Then, please compute the standard deviation of forecast error using the first eight months.

Months Demand Forecast

$1210222$

$2240235$

$3230225$

$4240245$

$5280265$

$6222250$

$7220220$

$8250273$

$6.$ Below are a pharmacy$$s actual sales and forecasted demand for a certain prescription drug for $5$ months. How accurate is their forecast? Calculate MAD and MSE and create a control chart.

Months Actual sales Forecasted demand

$1215$ n$/$a

$2235255$

$3200203$

$4305325$

$5310320$

$7.$ Freight car loadings during a $14-$week period at a port are:

Week Number Week Number

$12328385$

$22509420$

$327010465$

$426211485$

$532012498$

$635213520$

$737514555$

a$)$ Compute a linear trend line for freight car loadings using of Excel$$s Trendline, with display Equation on chart option.

b$)$ Use the trend equation to predict loadings for weeks $15$ and $16.$

$8.$ Use of simpler linear regression analysis assumes that:

a$)$ Variations around the line are non$-$random.

b$)$ A straight line will be determined that maximizes the sum of deviations of the data points.

c$)$ Predictions are to be made only within the range of observed values of the predictor variable.

d$)$ Deviations around the line are not normally distributed.

e$)$ Predictions can be made outside the range of observed values of the predictor variable.

$9.$ Please answer the following True or False questions.

a$)$ When error values fall outside the limits of a control chart, this signals a need for corrective action. $($True$/$False$)$

b$)$ When all errors plotted on a control chart are either all positive, or all negative, this shows that the forecasting technique is performing adequately. $($True$/$False$)$

c$)$ A random pattern of errors within the limits of a control chart signals a need for corrective action. $($True$/$False$)$