Final answer:
The student is asked to determine correlation from a scatter plot, calculate and draw a line of best fit, find the slope and y-intercept values, identify the correlation coefficient, and assess the significance and appropriateness of the linear relationship modeled.
Step-by-step explanation:
To examine the type of correlation a scatter plot shows and to model the data, it is essential to understand how to numerically describe the relationship between two quantitative variables. The process typically involves several key steps:
- Draw a scatter plot of the given data to visually assess the relationship between the independent (x-axis) and dependent (y-axis) variables.
- Calculate the least-squares regression line using the formula ý = a + bx, where 'a' represents the y-intercept and 'b' the slope.
- Draw the line of best fit on the scatter plot to represent the trend in the data.
- Determine the correlation coefficient (r-value), which quantifies the strength and direction of a linear relationship between the two variables.
- Assess whether the correlation coefficient is statistically significant to verify the reliability of the linear model.
In a hypothetical data set regarding the average Consumer Price Index (CPI) for the year 1990, you would obtain the necessary measurements from the data and plot them accordingly. Afterwards, you would use statistical software or a calculator's regression function to find the equation of the least-squares regression line. This equation would then be added to the scatter plot.
The slope of the regression line illustrates the rate of change between variables, while the y-intercept represents the expected value of the dependent variable when the independent variable is zero.
An r-value of zero implies there is no linear relationship between the two variables.
Finally, it is crucial to inspect the scatter plot to decide whether a linear model is appropriate or if a different curve might be a better fit for the data, even if the correlation coefficient is significant.