"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Regression Line Find and draw the regression line."

검증된 단계별 안내

Step 1: Organize the data into two variables: the independent variable (year, x) and the dependent variable (average age of vehicles, y). The data points are: (2014, 11.4), (2015, 11.5), (2016, 11.6), (2017, 11.7), (2018, 11.7), (2019, 11.8), (2020, 11.9), (2021, 12.1).

Step 2: Convert the years into a simpler numerical format for regression calculations. For example, let x = 0 represent 2014, x = 1 represent 2015, and so on up to x = 7 for 2021. This simplifies the data points to: (0, 11.4), (1, 11.5), (2, 11.6), (3, 11.7), (4, 11.7), (5, 11.8), (6, 11.9), (7, 12.1).

Step 3: Use the formula for the slope of the regression line, m = (Σ(x*y) - n*mean(x)*mean(y)) / (Σ(x^2) - n*mean(x)^2), where n is the number of data points, Σ represents summation, and mean(x) and mean(y) are the averages of x and y respectively.

Step 4: Calculate the y-intercept of the regression line using the formula b = mean(y) - m*mean(x), where m is the slope calculated in Step 3.

Step 5: Write the equation of the regression line in the form y = mx + b, where m is the slope and b is the y-intercept. Plot the regression line on a graph with the given data points to visualize the trend.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Regression Line

A regression line is a statistical tool used to model the relationship between two variables by fitting a linear equation to observed data. In this context, it helps to predict the average age of vehicles based on the year. The line is determined by minimizing the distance between the data points and the line itself, providing insights into trends over time.

Dependent and Independent Variables

In regression analysis, the dependent variable is the outcome we are trying to predict or explain, while the independent variable is the predictor or input. Here, the average age of vehicles (y) is the dependent variable, and the year (x) is the independent variable. Understanding this distinction is crucial for interpreting the regression results correctly.

Correlation

Correlation measures the strength and direction of a linear relationship between two variables. A positive correlation indicates that as one variable increases, the other also tends to increase. In this scenario, analyzing the correlation between the year and the average age of vehicles can help determine if older vehicles are becoming more common over time.

"Old Vehicles In Exercises 31–34, use the figure shown at the left.Regression Line Find and draw the regression line."