Question

1. you and your friend are working on a group project. your partner did all the mathematical calculations on a graphing calculator. it is now your turn to complete parts 2 and 4 below to draw conclusions based on your partners work. (lesson 14.2) the table below shows the total attendance at major - league baseball games, at 10 - year intervals since 1930. use the table for the problems that follow. round all answers to the nearest thousandth. major league baseball total attendance (y), in millions, in years since 1930 (x) x 0 10 20 30 40 50 60 70 80 y 10.1 9.8 17.5 19.9 28.7 43.0 54.8 72.6 73.1 part 1: use a graphing calculator to find the linear regression, quadratic regression, and exponential regression for the data. then graph all three models. y = 0.897x + 0.738 y = 0.007x² + 0.304x + 7.654 y = 11.504·1.025^x part 2: which model is a good fit for the data? explain by comparing the three graphs. (1 point) part 3: use each regression model to predict major - league baseball attendance for year 2020. linear: 81.5 million in attendance quadratic: 91.7 million in attendance exponential: 120.4 million in attendance part 4: which prediction seems the most likely? explain by comparing the three predicted baseball attendances. how can you accurately know which regression model is the best fit? (1 point)

Explanation:

Part 2:

Step1: Observe data trend

The data shows non - linear growth.

Step2: Analyze models

Linear is too constant, exponential is too fast. Quadratic fits better.

Part 4:

Step1: Evaluate predictions

Linear may underestimate, exponential may over - estimate.

Step2: Determine best fit method

Use $R^{2}$ value for accuracy.

Answer:

Part 2:

The quadratic model $y = 0.007x^{2}+0.304x + 7.654$ is a good fit for the data. The data points seem to follow a curved - upward trend more closely compared to the linear model which has a more constant rate of change and the exponential model which seems to grow too rapidly at the end. The quadratic model captures the initial slow growth and then the steeper increase better.

Part 4:

The quadratic prediction of 91.7 million seems the most likely. The linear model might underestimate the growth as it has a constant slope and doesn't account for the accelerating growth trend. The exponential model might over - estimate as it grows very rapidly. To accurately know which regression model is the best fit, we can calculate the coefficient of determination ($R^{2}$) value for each model. A value closer to 1 for $R^{2}$ indicates a better fit.