the cantril ladder is a 0 - 10 scale used to rate life satisfaction. the scatterplot shows a countrys…

the cantril ladder is a 0 - 10 scale used to rate life satisfaction. the scatterplot shows a countrys national average cantril ladder score on the horizontal axis and the countrys gross domestic product (gdp), in dollars, per capita on the vertical axis for 141 different countries.\na. three possible models for the data are created. each models computer output and residual plot are shown. which of the three models is best? why?\nb. determine the equation for your chosen model. be sure to define any variables used.\nc. use your chosen model to predict the gross domestic product per capita for a country with an average cantril ladder score of 7.2.\nd. the country with an average cantril ladder score of 7.2 has a gdp per capita of $48,678.68. using the prediction from part c, calculate and interpret the residual.

the cantril ladder is a 0 - 10 scale used to rate life satisfaction. the scatterplot shows a countrys national average cantril ladder score on the horizontal axis and the countrys gross domestic product (gdp), in dollars, per capita on the vertical axis for 141 different countries.\na. three possible models for the data are created. each models computer output and residual plot are shown. which of the three models is best? why?\nb. determine the equation for your chosen model. be sure to define any variables used.\nc. use your chosen model to predict the gross domestic product per capita for a country with an average cantril ladder score of 7.2.\nd. the country with an average cantril ladder score of 7.2 has a gdp per capita of $48,678.68. using the prediction from part c, calculate and interpret the residual.

Answer

Explanation:

Step1: Select best - model

The best model is the one with randomly - scattered residuals. By observing the residual plots of the three models, the model with the most randomly - scattered residuals is chosen as the best. This indicates that the model has minimized the systematic errors.

Step2: Determine model equation

Let (x) be the average Cantril Ladder score and (y) be the gross domestic product (GDP) per capita. From the computer output of the chosen model, we extract the coefficients to form the regression equation (y = a+bx) (where (a) is the intercept and (b) is the slope).

Step3: Make prediction

Substitute (x = 7.2) into the chosen model's equation (y=a + bx) to predict the GDP per capita.

Step4: Calculate residual

The residual (e) is calculated as (e=y_{actual}-y_{predicted}), where (y_{actual}=48678.68) and (y_{predicted}) is the value obtained in Step 3. A positive residual means the actual value is higher than the predicted value, and a negative residual means the actual value is lower than the predicted value.

Answer:

a. The model with randomly - scattered residuals in its residual plot is the best. b. Let (x) be the average Cantril Ladder score and (y) be the GDP per capita. The equation is (y=a + bx) (values of (a) and (b) are obtained from the computer output of the chosen model). c. Substitute (x = 7.2) into (y=a + bx) to get the predicted GDP per capita. d. Residual (e = 48678.68-y_{predicted}). If (e>0), the actual GDP per capita is higher than predicted; if (e < 0), the actual GDP per capita is lower than predicted.