Orders have to be placed the day before receipt, so they're concerned that they're not ordering enough. Han Solo and his accountant Chewbacca are sitting down and looking at the numbers, trying to figure things out... when there's a flash of light, and Force Ghost Yoda appears!

Force Ghost Yoha yells, "YEEEEEAAAAAAAAAAHHHHH, BOOOOOOOIIIIIIIIIZE!!" Chewie looks at Han and says, "ARRRBLEWHARRBLEGARRRBLE?" Han replies, "Yeah $-$ I liked him better when he talked authentic Yoda Gibberish, too."

"That's not important now," Force Ghost Yoda says. "What you need is a good method of forecasting based on how your business is growing. Let's see how much Porg Sausage you've used for the past couple of weeks."

Here's what they recorded for the past $14$ days:

Day Pounds of Porg Sausage Used

$111$

$211$

$314$

$413$

$515$

$616$

$718$

$819$

$919$

$1018$

$1120$

$1221$

$1324$

$1424$

Stimulus for question at position: $1$

The following text applies to the questions at positions $1$

Exponential Smoothing Part $1-$ The Naive Forecast

"We're gonna use a method called Exponential Smoothing," Force Ghost Yoda told them, but that starts with the prior period's forecast. We don't have that for Day, so we have to stipulate what the forecast is$.$ We'll make it equal to that day's actual number $-$ something called a Naive Forecast."

Day Pounds of Porg Sausage Used Porg Sausage Forecast

$111$ GOLF

$211$

$314$

$413$

$515$

$616$

$718$

$819$

$919$

$1018$

$1120$

$1221$

$1324$

$1424$

Question at position $1$

$1$

$1\mathrm{.}6$ points

Question at position $1$

What is the Na$$ve Forecast that should be in cell GOLF?

What is the Na$$ve Forecast that should be in cell GOLF?

$-2$

$11$

$10$

$9$

Stimulus for question at position: $2$

The following text applies to the questions at positions $2$

Exponential Smoothing Part $2-$ The Forecast Deviation

"Now," Force Ghost Yoda said, $"$we need to calculate the Forecast Deviation for Day $1-$ the Actual value minus the Forecast value. That's pretty easy!"

Day Pounds of Porg Sausage Used Porg Sausage Forecast Forecast Deviation

$111$ GOLF HOTEL

$211$

$314$

$413$

$515$

$616$

$718$

$819$

$919$

$1018$

$1120$

$1221$

$1324$

$1424$

Question at position $2$

$2$

$1\mathrm{.}6$ points

Question at position $2$

What is the Forecast Deviation that should be in cell HOTEL?

What is the Forecast Deviation that should be in cell HOTEL?

$11$

$-11$

$0$

$3\mathrm{.}141592653589793238462643383279502884197$

Stimulus for question at position: $3$

The following text applies to the questions at positions $3$

Exponential Smoothing Part $3-$ Picking an Alpha Value

"Next," Force Ghost Yoda said, $"$we need to pick a smoothing constant $-$ called alpha. Alpha needs to be a decimal number between $0$ and $1.$ Let's pick a value in the middle!"

Alpha $=$ INDIA

Day Pounds of Porg Sausage Used Porg Sausage Forecast Forecast Deviation

$111$ GOLF HOTEL

$211$

$314$

$413$

$515$

$616$

$718$

$819$

$919$

$1018$

$1120$

$1221$

$1324$

$1424$

Question at position $3$

$3$

$1\mathrm{.}6$ points

Question at position $3$

Based on Force Ghost Yoda's recommendation, what is the best value for Alpha that should be in cell INDIA? $($round to $2$ digits$)$

Based on Force Ghost Yoda's recommendation, what is the best value for Alpha that should be in cell INDIA? $($round to $2$ digits$)$

$0\mathrm{.}999999998027$

$0\mathrm{.}10$

$0\mathrm{.}90$

$0\mathrm{.}50$

Stimulus for question at position: $4$

The following text applies to the questions at positions $4$

Exponential Smoothing Part $4-$ Using Smoothing to Forecast Day $2$

"Finally," Force Ghost Yoda said, $"$we can calculate the smoothed Forecast for Day $2.$ To do this, we multiply that alpha value times the Deviation of Day $1-$ the previous period $-$ then add it to the Forecast for Day $1.$ Again, this one is easy!"

Alpha $=$ INDIA

Day Pounds of Porg Sausage Used Porg Sausage Forecast Forecast Deviation

$111$ GOLF HOTEL

$211$ JULIET

$314$

$413$

$515$

$616$

$718$

$819$

$919$

$1018$

$1120$

$1221$

$1324$

$1424$

Question at position $4$

$4$

$1\mathrm{.}6$ points

Question at position $4$

What would the exponentially smoothed forecast be for Day $2$ in cell JULIET?

What would the exponentially smoothed forecast be for Day $2$ in cell JULIET?

$12$

$11$

$10$

$9$

Stimulus for questions at positions: $5,6$

The following text applies to the questions at positions $5,6$

Exponential Smoothing Part $5-$ Using Smoothing to Forecast Day $3$

"You've got this!", Ghost Force Yoda cried. "Now, you go ahead and calculate the forecast for Day $3$ without my help. Remember, now Day $2$ is the prior forecast day that we have to use in our calculations!"

Alpha $=$ INDIA

Day Pounds of Porg Sausage Used Porg Sausage Forecast Forecast Deviation

$111$ GOLF HOTEL

$211$ JULIET KILO

$314$ LIMA

$413$

$515$

$616$

$718$

$819$

$919$

$1018$

$112$