Final answer:
To plot and analyze the average price of black bags by year, data is entered into a calculator or spreadsheet, and a scatter plot is created with a trendline and r-squared value. The line of best fit is calculated, drawn, and then evaluated for its correlation coefficient and coefficient of determination, indicating how well it predicts outcome variables. In this case, the r-squared value is approximately 0.83.
Step-by-step explanation:
Plotting and Analyzing the Average Price of Black Bags by Year
To plot the average price of black bags by year, you will need to start by entering the data into a calculator or spreadsheet program capable of creating scatter plots. Once the data is entered, you can generate a scatter plot with the date on the horizontal axis and the average price on the vertical axis.
To calculate the line of best fit, which is the least-squares regression line, you can use the regression function in the calculator or spreadsheet program. The equation of this line is generally written in the form ý = a + bx, where 'a' represents the y-intercept and 'b' represents the slope of the line. Once you have this equation, you should draw the line on your scatter plot.
After adding the trendline, you can calculate the correlation coefficient, commonly denoted as 'r,' which measures the strength and direction of the linear relationship between the two variables in your plot. If 'r' is significantly far from 0, it suggests that there is a significant correlation. However, we are often more interested in the coefficient of determination, expressed as r², which indicates the proportion of variance in the dependent variable that can be predicted from the independent variable. The closer the r² value is to 1, the better the fit of our regression line to the data.
In your specific case, the new slope is 7.39 with an R-value of 0.9121, indicating a strong correlation and that the line can better predict the outcome variables. The r², or coefficient of determination, would be approximately 0.83 (since 0.9121 squared is approximately 0.83), suggesting that about 83% of the variation in the dependent variable can be explained by the independent variable. Lastly, the average CPI for 1990 or the predicted value at a certain point can be calculated using the regression line equation by plugging in the specific year into the 'x' variable.