Question

Assume that the initial forecast for may is 85,300 and the initial trend adjustment is 0. the smoothing constants selected are α ​= 0.2 and β ​= 0.2.

Answer 1

Using the given simple linear regression equation, sales on day 60 are predicted to be 250.12 thousand dollars, and on day 90, the predicted sales are 324.52 thousand dollars. Extrapolation beyond the observed data range should be done with caution as it can lead to unreliable results.

Step-by-step explanation:

Forecasting Sales with Regression Analysis

The student's question pertains to using a simple linear regression model to predict sales growth for an electronics retailer. Given the regression equation ŷ = 101.32 + 2.48x, where x represents the day and ŷ the sales in thousands of dollars, we can make sales predictions for specific days.

To predict the sales on day 60, substitute x = 60 into the regression equation:
ŷ = 101.32 + 2.48 (60) = 101.32 + 148.8 = 250.12 thousand dollars.

The predicted sales on day 90 are found by substituting x = 90 into the equation:
ŷ = 101.32 + 2.48 (90) = 101.32 + 223.2 = 324.52 thousand dollars.

It is important to note that these predictions are best applied within the range of observed data values. Predicting outside this range, such as for an x value not within the observed period, may lead to unreliable results and is known as extrapolation.