Historical demand for a product is shown below. Using the regression equation in part (d), calculate the forecast for July.

	DEMAND
January	12
February	11
March	15
April	12
May	16
June	15

Historical demand for a product is as follows. Using simple linear regression, calculate the trend line for the historical data. Let's say the $X$ axis is April $=1$, May $=2$, and so on, while the $Y$ axis is demand.

Historical demand for a product is as follows. Using a simple four-month moving average, calculate a forecast for October.

Historical demand for a product is

$$\begin{aligned} &\text { Demand }\\ &\begin{array}{lc} \hline \text { January } & 12 \\ \text { February } & 11 \\ \text { March } & 15 \\ \text { April } & 12 \\ \text { May } & 16 \\ \text { June } & 15 \\ \hline \end{array} \end{aligned}$$

a. Using a weighted moving average with weights of $0.60,0.30$, and $0.10$, find the July forecast.

b. Using a simple three-month moving average, find the July forecast.

c. Using single exponential smoothing with $\alpha=0.2$ and a June forecast $=13$, find the July forecast. Make whatever assumptions you wish.

d. Using simple linear regression analysis, calculate the regression equation for the preceding demand data.

e. Using the regression equation in d, calculate the forecast for July.

Historical demand for a product is shown below. Using single exponential smoothing with $\alpha=0.2$ and a June forecast = 13, find the July forecast. Make whatever assumptions you wish.

Historical demand for a product is as follows. Using single exponential smoothing with $\alpha=0.2$ and a September forecast $=65$, calculate a forecast for October.

Historical demand for a product is as follows.

$$\begin{aligned} &\text { Demand }\\ &\begin{array}{ll} \hline \text { April } & 60 \\ \text { May } & 55 \\ \text { June } & 75 \end{array} \end{aligned}$$

$$\begin{aligned} &\text { Demand }\\ &\begin{array}{lc} \hline \text { July } & 60 \\ \text { August } & 80 \\ \text { September } & 75 \\ \hline \end{array} \end{aligned}$$

a. Using a simple four-month moving average, calculate a forecast for October.

b. Using single exponential smoothing with $\alpha=0.2$ and a September forecast $=65$, calculate a forecast for October.

c. Using simple linear regression, calculate the trend line for the historical data. Let's say the $X$ axis is April $=1$, May $=2$, and so on, while the $Y$ axis is demand.

d. Calculate a forecast for October using your regression formula.

Complete the problems. Check your answers in the back of the book.

Use an $18$-inch, $10$-inch, and $7$-inch length of board to mark off a length of $15$ inches.

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Describe the differences between estimating the mean value of $y$ and using a regression model to forecast a specific value of $y$.