High School

A forecaster develops a linear regression model for quarterly sales data shown in the table. The slope of the regression equation is 37.9, and the intercept is 57. Use the regression model to determine the seasonal index for the third quarter.

1) 0.99
2) 1.12
3) 0.93
4) 1.09

Answer :

Final answer:

To determine the seasonal index for the third quarter using the regression model, substitute x = 3 into the equation ŷ = 37.9x + 57. Divide the predicted sales for the third quarter by the average sales for all quarters to find the seasonal index.

Explanation:

To determine the seasonal index for the third quarter, we can use the regression model. The regression model is represented by the equation ŷ = 37.9x + 57, where ŷ is the predicted value for sales and x represents the quarter. Since we want to find the seasonal index for the third quarter, we substitute x = 3 into the equation: ŷ = 37.9(3) + 57 = 113.7.

If we divide the predicted sales for the third quarter by the average sales for all quarters, we can find the seasonal index: 113.7 / (the average of all sales) = seasonal index. The correct answer is not provided in the options.

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