Question

Consider the following table containing unemployment rates for a 10-year period. Unemployment Rates Year Unemployment Rate (%) 1 4.7 2 6.8 3 10.8 4 11.5 5 6.9 6 11.7 7 8.7 8 7.4 9 10.7 10 11.1 Step 2 of 2 : What is the coefficient of determination for the regression model? Round your answers to two decimal places.

Answer 1

The answer is in this explanation below, scroll down !! :>

Explanation:

To calculate the coefficient of determination for the regression model, we first need to perform a linear regression analysis on the given data. The coefficient of determination, denoted as R^2, represents the proportion of the variance in the dependent variable (unemployment rates) that can be explained by the independent variable (years).

Here are the steps to find the coefficient of determination:

1. Calculate the mean of the unemployment rates. Add up all the rates and divide by the total number of rates (10 in this case). The mean unemployment rate is 8.64%.

2. Calculate the sum of squares total (SST), which measures the total variation in the dependent variable. To do this, subtract the mean unemployment rate from each rate, square the differences, and sum them up. SST = (4.7 - 8.64)^2 + (6.8 - 8.64)^2 + ... + (11.1 - 8.64)^2.

3. Perform a linear regression analysis to find the regression equation that best fits the data. This equation will give us the predicted values for the unemployment rates based on the years.

4. Calculate the sum of squares regression (SSR), which measures the variation in the dependent variable that is explained by the regression equation. To do this, subtract the predicted unemployment rate for each year from the mean unemployment rate, square the differences, and sum them up. SSR = (predicted rate1 - mean rate)^2 + (predicted rate2 - mean rate)^2 + ... + (predicted rate10 - mean rate)^2.

5. Calculate the coefficient of determination (R^2) using the formula: R^2 = SSR / SST. Divide the sum of squares regression (SSR) by the sum of squares total (SST).

6. Round the coefficient of determination to two decimal places.

By following these steps, you can calculate the coefficient of determination (R^2) for the regression mode!

Answer 2

Step-by-step explanation: 1.5