Determine if a linear relationship exists between unemployment rates and cost of living indexes by constructing a scatter chart and adding a trend line. What is the regression model and R2?
To determine if a linear relationship exists between unemployment rates and cost of living indexes, you can follow these steps:
1. Collect the data: Gather data on unemployment rates and cost of living indexes for a set of observations (e.g., different cities or time periods). Ensure that you have corresponding values for both variables.
2. Create a scatter chart: On a graph, plot the unemployment rates on the x-axis and the cost of living indexes on the y-axis. Each observation will be represented by a point on the chart.
3. Add a trend line: In most graphing software or spreadsheet tools, you can add a trend line to your scatter chart. The trend line will help visualize any potential linear relationship between the two variables.
4. Determine the regression model: Once the trend line is added, it can provide the regression equation. The regression model represents the linear relationship between the two variables. It will be in the form of: y = mx + b, where y represents the cost of living index, x represents the unemployment rate, m is the slope of the line, and b is the y-intercept.
5. Calculate R-squared (R²): R-squared (R²) is a measure of how well the regression model fits the data. It quantifies the proportion of the variance in the dependent variable (cost of living index) that is predictable from the independent variable (unemployment rate). R² ranges from 0 to 1, where 0 indicates no linear relationship and 1 indicates a perfect fit.
To calculate R², you can use the following formula:
R² = (SSR/SST), where SSR represents the sum of the squared residuals (the difference between the observed y values and the predicted y values), and SST represents the total sum of squares (the difference between the observed y values and the mean y value).
By following these steps, you can determine if there is a linear relationship between unemployment rates and cost of living indexes and obtain the regression model and R² value.