Final answer:
The problems denote classification rather than regression since they involve predicting categorical outcomes (approval of loan, win or loss of a sports series). A scatter plot, least-squares line, and the correlation coefficient are used to understand the relationships between variables in a regression analysis.
Step-by-step explanation:
The student is presented with two problems to determine whether they are cases of regression or classification: Given a set of loan applications with approval status, predicting if a new application should be approved is a classification problem because the outcome is a category (approved or not approved), not a continuous number Predicting if Bangladesh wins the current series against England based on match detail is also a classification problem since the outcome is a binary result: win or loss. In terms of standard statistical approaches: The independent variable could be various features of the loan application, while the dependent variable is the approval status.
The independent variable could be the match details like scores, players' performance, etc., and the dependent variable would be the series result. A scatter plot is a type of plot or mathematical diagram that uses Cartesian coordinates to display values for two variables for a set of data. When constructing one, data that potentially model a linear relationship between variables is considered. The least-squares line, shown as ý = a + bx, and the correlation coefficient provide insight into the strength and nature of the relationship between variables. In a regression analysis, determining the line of best fit and its slope and y-intercept can help us understand the relationship between the variables and make predictions, such as estimating average heights based on age or predicting outcomes like crime rates when examining causative factors.