7. Your boss assigns you a task to estimate the relationship between per capita income

and the percentage of labor force employed in the agricultural sector in ten
developing countries. Your data are:
Country A B C D E F G H I J
Per capital income (Y) 6 8 8 7 7 12 9 8 9 10
% Labor force in
agriculture
9 10 8 7 10 4 5 5 6 7
i. Plot the observation on the scatter and describe the pattern ofrelationship.
ii. What is the nature of the data set?
iii. Calculate the intercept and slope coefficients, and the coefficient of
determination.
iv. If the percent of the labor force in agriculture in another developingcountry was
8 percent, what level of per capita income (in thousands of U.S. dollars) would
you estimate that country had?
v. What level of labor should be used in agriculture to maintain per capital income at 13 (thousands USD)

i. To plot the observation on the scatter and describe the pattern of relationship, you can follow these steps:

1. Create a scatter plot with the x-axis representing the percentage of the labor force in agriculture and the y-axis representing the per capita income.
2. Plot the observations for each country on the scatter plot, using the given data points.
3. Observe the cluster of points on the scatter plot. Look for any visible patterns, trends, or relationships between the variables.

ii. The nature of the data set can be determined by analyzing the scatter plot. Based on the scatter plot, you can determine whether there is a positive, negative, or no relationship between the variables. Let's analyze the scatter plot to determine the nature of the data set.

iii. To calculate the intercept and slope coefficients, as well as the coefficient of determination, you can use linear regression analysis. Here's how you can do it:

1. Create a linear regression model using the given data points for per capita income (Y) and the percentage of the labor force in agriculture.
2. Calculate the intercept and slope coefficients of the linear regression model.
3. Calculate the coefficient of determination (R-squared value) to measure the goodness of fit of the regression model.

iv. To estimate the per capita income if the percent of the labor force in agriculture in another developing country was 8 percent, you can use the linear regression model's equation and substitute the value of 8 percent into the equation.

v. To determine the level of labor that should be used in agriculture to maintain a per capita income of 13 (thousands USD), you can rearrange the linear regression equation, substitute the desired per capita income value, and solve for the percentage of the labor force in agriculture.