The scatterplot above shows the grocery store sales in the United States, in billions of dollars, for selected years from 2000 to 2016. Also shown is a trend line for the data with equation y = 14.1x + 369.9, which is used to predict the grocery store sales, y, in billions of dollars, in the United States x years after 2000. Based on the equation of the trend line, how much more, in billions of dollars, are the predicted grocery store sales in the United States in year 2023 than in year 2000?
Predicted grocery store sales in the United States in year 2023 exceed those in year 2000 by 324.3 billion dollars.
To determine this difference, we can use the trend line equation \(y = 14.1x + 369.9\). For the year 2000, \(x = 0\) and for the year 2023, \(x = 23\). By calculating the sales for both years and finding the difference, we can arrive at the correct answer.
This value represents an underestimation of the predicted increase in grocery store sales between 2000 and 2023. When substituting \(x = 23\) into the equation, the sales for 2023 are calculated to be much higher than this figure, indicating that the increase is not accurately reflected in this choice.
This choice correctly reflects the increase in predicted grocery store sales. By substituting \(x = 0\) for the year 2000, we find the sales to be \(369.9\) billion dollars. For 2023, substituting \(x = 23\) yields \(694.2\) billion dollars. The difference \(694.2 - 369.9 = 324.3\) billion dollars, confirming this as the correct answer.
This option suggests a larger increase than what the trend line predicts. The calculations for sales in both years do not support this figure, as it exceeds the actual computed difference based on the trend line's equation.
This choice implies an unrealistic increase in sales that is not supported by the trend line's equation. The predicted sales figures calculated for both years do not yield a difference close to this value, indicating a significant overestimation.
This figure represents the total predicted sales for the year 2023 rather than the increase from 2000 to 2023. It misinterprets the question, as it does not account for the initial sales figure from the year 2000, leading to an inaccurate representation of the increase.
To summarize, the predicted increase in grocery store sales from 2000 to 2023, calculated using the provided trend line equation, is accurately represented by the value of 324.3 billion dollars. This shows the effectiveness of linear regression in forecasting sales trends over time, helping businesses and analysts make informed decisions based on historical data and predicted growth.
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