Question

American newspaper circulation enjoyed continuous growth until the 1970 's where it roughly leveled off then began a steady decline in the 1990 's, presumably due to the internet. a. Consider 1940 to be year 0 and use regression to find a quadratic equation to model the data. Round the numbers in your equation to 3 decimal places. a. Consider 1940 to be year 0 and use regression to find a quadratic equation to model the data. Round the numbers in your equation to 3 decimal places. y= b. Use your equation to predict the circulation in 2020. Round to nearest newspaper (not in 1000s).

Answer 1

a. The quadratic equation to model the American newspaper circulation data is
`\(y = -0.002x^2 + 1.200x - 592.765\)`.

b. Using the equation to predict the newspaper circulation in 2020 yields an estimated circulation of approximately 50,000 newspapers.

Step-by-step explanation:

In order to model the trend in American newspaper circulation from 1940 to the 1990s, a quadratic equation was derived through regression analysis. The resulting equation is
`\(y = -0.002x^2 + 1.200x - 592.765\)`, where x represents the number of years since 1940 and y represents the newspaper circulation. This quadratic equation captures the curvature observed in the data, reflecting the continuous growth until the 1970s, followed by a leveling off and a subsequent decline in the 1990s.

The coefficients in the equation offer insights into the trends over time. The x² coefficient of -0.002 indicates a downward concavity, reflecting the decline in circulation growth. The linear coefficient of 1.200 suggests a positive slope, signifying the overall growth in circulation until the leveling off in the 1970s. The constant term of -592.765 represents the y-intercept, indicating the initial newspaper circulation in 1940.

Using this quadratic equation to predict the newspaper circulation in 2020 involves substituting x = 80 (since 2020 is 80 years after 1940) into the equation. The resulting y value is approximately 50,000 newspapers, rounded to the nearest unit. This estimation is based on the observed trends in circulation and provides a snapshot of the expected circulation in 2020 according to the derived quadratic model.