Problems $1-2$ refer to the following: $($Please calculate up to $4$ decimal places$)$

Demand for the last three months was:

Month

Demand

January

$140$

February

$160$

March

$170$

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Suppose the estimated simple regression equation in the given data is Y $=110+20$X$.$

Assume that the smoothing constants selected are $$and$.$

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$1.$ Predict demand for February using Holt$$s model based on $(2$ points$)$

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$2.$ Suppose L$3=175$ and T$3=18,$ and predict demand for June using Holt$$s model based on $(2$ points$)$

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Problems $3-5$ refer to the following: $($Please calculate up to $4$ decimal places$)$

Demand for the last ten years was:$($For $2015$ and $2016,$ use your calculator to forecast so you know how to use formulas, and for the rest, use Excel to calculate and find the answers.$)$

Year

$2015$

$2016$

$2017$

$2018$

$2019$

$2020$

$2021$

$2022$

$2023$

$2024$

Demand

$1368$

$1380$

$1406$

$1439$

$1474$

$1499$

$1528$

$1541$

$1570$

$1608$

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$3.$ Predict demand for the year $2020$ using Holt$$s model with $(2$ pts$)$

$($ Calculate $2015$ and $2016$

$4.$ Predict demand for the year $2034$ using Holt$$s model with $.(2$ pts$)$

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$5.$ Predict demand for the year $2020$ using Holt$$s model with an optimal $$and $(4$ pts$)$

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Problem $6$:$$ Quarterly water usage is shown below. $($Please calculate up to $4$ decimal places.$)$

$$ Year$$ Q$1$ Q$2$ Q$3$Q$4$

$2023410615$

$2024311714$

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Suppose we obtain the following regression model based on Q$1,$ Q$2,$ Q$3,$ and Q$4$ using the data in the table above: $$Y $=5+2*$Q$1+8*$Q$23*$Q$3$

Forecast the quarter $3($Q$3)$ water usage for the year $2030.(2$ pts$)$

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Problem $7-8$:$$ Quarterly billing for water usage is shown below. $($Please calculate up to $4$ decimal places$)$

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Year

Quarter

$$ Q$1$

$$ Q$2$

$$Q$3$

$$Q$4$

$2023$

$164$

$170$

$188$

$153$

$2024$

$86$

$95$

$104$

$71$

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$7.$ Which time series forecasting method best fits the given data $($Plot data and see the pattern of data$)?(2$ pts$)$

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$8.$ Forecast the quarter $2($Q$2)$ of the year $2025.(4$pts$)$