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To calculate the next forecast, you use the weighted average form of the exponential smoothing formula: $F_{t+1} = \alpha A_t + (1 - \alpha)F_t$. With a smoothing constant of $\alpha = 0.2$, the formula becomes $F_{t+1} = 0.2(A_t) + 0.8(F_t)$.

Conditions: The smoothing constant is $\alpha = 0.2$.; You know the actual sales value for the current period ($A_t$).; You know the forecast value for the current period ($F_t$).

To calculate the next forecast, you use the weighted average form of the exponential smoothing formula: $F_{t+1} = \alpha A_t + (1 - \alpha)F_t$. With a smoothing constant of $\alpha = 0.2$, the formula becomes $F_{t+1} = 0.2(A_t) + 0.8(F_t)$.

Conditions: The smoothing constant is $\alpha = 0.2$.; You know the actual sales value for the current period ($A_t$).; You know the forecast value for the current period ($F_t$).

The intercept $b_0$ is calculated by substituting the mean point $(\bar{x}, \bar{y})$ and the known slope $b_1$ into the regression equation $\hat{y} = b_0 + b_1x$, and then solving algebraically for $b_0$. In the example, substituting $x=3$, $\hat{y}=4$, and $b_1=0.6$ yields $4 = b_0 + 0.6(3)$, which simplifies to $b_0 = 2.2$.

Conditions: The slope $b_1$ has already been computed.; The sample means $\bar{x}$ and $\bar{y}$ are known.; The regression line is assumed to pass through $(\bar{x}, \bar{y})$.

The intercept $b_0$ is calculated by substituting the mean point $(\bar{x}, \bar{y})$ and the known slope $b_1$ into the regression equation $\hat{y} = b_0 + b_1x$, and then solving algebraically for $b_0$. In the example, substituting $x=3$, $\hat{y}=4$, and $b_1=0.6$ yields $4 = b_0 + 0.6(3)$, which simplifies to $b_0 = 2.2$.

Conditions: The slope $b_1$ has already been computed.; The sample means $\bar{x}$ and $\bar{y}$ are known.; The regression line is assumed to pass through $(\bar{x}, \bar{y})$.

To calculate the Mean Squared Error (MSE), you first find the forecast errors by subtracting the forecast from the actual sales for each period. Next, you square each of these errors.

Conditions: You have calculated the forecasts for each period.; You have the actual sales data for each period.; Errors are not calculated for the first period if $F_1 = A_1$.

To calculate the Mean Squared Error (MSE), you first find the forecast errors by subtracting the forecast from the actual sales for each period. Next, you square each of these errors.

Conditions: You have calculated the forecasts for each period.; You have the actual sales data for each period.; Errors are not calculated for the first period if $F_1 = A_1$.