Question

A new department store opened in January 2016. A graph of the income in the first several months is included below:

Considering the graph above, could we use this linear model to predict income of January 2025? Complete the sentence below by selecting the best of the available phrases.
[ Select ] ["No", "Yes"] because [ Select ] ["we have one year of data and 2025 is 9 years beyond the scope of the model.", "this store is losing money and certain to be closed by 2025.", "we have 12 data points and 2025 is only 9 years into the future."]

Answer 1

No. The linear model cannot be used to predict the sales income of January 2025 because we have one year of data, and 2025 is nine years beyond the model's scope.

A linear model is an equation or mathematical formula that estimates the relationship between one independent quantitative variable and one dependent quantitative variable using a straight line.

The linear model can be written as y = mx + b, where m is the slope, x is a constant, and b is the y-intercept.

In this situation, the linear equation is written as y = -69.266x + 13250 to model the income of the new store over 12 months.

In month 0, the income is 13,250. In month one, the sales income increased to $13,300 but continued to decrease at an average constant rate.

Thus, the correct option is No. because we have one year of data, and 2025 is nine years beyond the model's scope.