Write a simple linear regression line $($equation$).$ Define Y$,$ a$,$ b$,$ and x $($t$).$

Define r$,$ r squared, and adjusted r

Define MAD, MSE, MAPE, why these are important?

Among other services and products that Karl's Copiers provides, it sells and repairs photocopy machines. It is now the end of December, $2021$ and the manager needs to plan his service staffing for January, $2022.$ The manager first needs to forecast the number of service calls for January, $2022.$ Following are the record of service calls for the past $12$ months

Month

Number of Service Calls

Month

Number of Service Calls

January

$30$

July

$31$

February

$24$

August

$38$

March

$27$

September

$37$

April

$31$

October

$36$

May

$37$

November

$32$

June

$34$

December

$29$

You have been asked by the manager to help with the forecast for January, $2022.$ He has asked you to provide forecasts for January using the following two methods:

Weighted Moving Average

Exponential Smoothing

He has also asked you to determine which of these two forecasts he should select. To make this assessment, he has asked that you compare the actual number of service calls to what the forecasts would have been for November through December, $2021$ using each of the two methods.

i$)$ For the weighted moving average, using a two$-$period weighted moving average with a weight of $0\mathrm{.}65$ for the most recent month and the remaining weight$($s$)$ consistent with this forecasting method as we applied it$.$

ii$)$ For exponential smoothing, using an $\backslash$sigma $=0\mathrm{.}30,$ and using a starting forecast for July, $2021$ of $34.$

a$)$ Prepare a forecast for January, $2022$ using each of the two methods.

b$)$ Recommend which of these two methods the manager should use for January based on the results of evaluation of the forecasts for November through December. Your selection criteria must be based on one of the numerical evaluation methods we have learned this class. Only saying $$it is the easier method$$ is not acceptable.