The NC State Employees Credit Union $($NC SECU$)$ needs your assistance forecasting loan applications. NCSECU has recorded the number of applications received each business day for the past $5$ weeks in the table below. NCSECU is only open to receive applications Monday $-$ Friday.

Week Day Period Demand

$1$ Mon $1547$

$1$ Tue $2335$

$1$ Wed $3420$

$1$ Thu $4464$

$1$ Fri $5760$

$2$ Mon $6593$

$2$ Tue $7414$

$2$ Wed $8449$

$2$ Thu $9499$

$2$ Fri $10737$

$3$ Mon $11634$

$3$ Tue $12395$

$3$ Wed $13582$

$3$ Thu $14483$

$3$ Fri $15742$

$4$ Mon $16674$

$4$ Tue $17488$

$4$ Wed $18608$

$4$ Thu $19544$

$4$ Fri $20843$

$5$ Mon $21737$

$5$ Tue $22507$

$5$ Wed $23556$

$5$ Thu $24576$

$5$ Fri $25986$

Rounding instructions

Carry your calculations to at least $3$ decimal places.

Enter all estimates for seasonal indices and regression coefficients $($e$.$g$.$ intercept and slope$)$ rounded to $3$ decimal places.

Round your final forecasts to one decimal place.

Method $1$: Simple Regression using Seasonal Indices

Calculate the seasonal indices

Deseasonalize the demand using the seasonal indices from Step $1$

Estimate a simple regression that predicts the deseasonalized demand based on the time period.

Use the simple regression to forecast the deseasonalized demand.

Reseasonalize the forecasts using the seasonal indices from Step $1.$

Seasonal Indices. Enter each seasonal index in decimal form rounded to three decimals.

Mon. Index:

Tue. Index:

Wed. Index:

Thu. Index:

Fri. Index:

Enter your regression equation that predicts the deseasonalized demand.

Forecast in Period t $=$ Ft $=$ intercept $+$ slope$*$t $=$

$+$

$*$t

Method $2$: Multiple Regression with Categorical Variables

Perform a multiple regression that predicts actual demand $($response variable$)$ as a function of the time period and the indicator variables for Mon $-$ Thu.

Remember that we must omit one categorical dummy variable to avoid problems with multicollinearity.

Omit the summary variable for Friday as your base case to match the solution.

Enter your multiple regression equation.

Forecast in Period t $=$ Ft $=$ intercept $+$ coefficient$*$t $+$ coefficient$*$Mon $+$ coefficient$*$Tue $+$ coefficient$*$Wed $+$ coefficient$*$Thu $=$

$+$

$*$t $+$

$*$Mon $+$

$*$Tue $+$

$*$Wed $+$

$*$Thu

Fill in the table below to complete two different forecasts that incorporate both trend and seasonality

Week Day Period

Method $1$ Final $($reseasonalized$)$ Forecast

Method $2$ Final Forecast

$6$ Mon $26$

$6$ Tue $27$

$6$ Wed $28$

$6$ Thu $29$

$6$ Fri $30$