[DATA] Credit Scores [See Problem 12 in Section 12.3] An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The data represent the interest rate (in percent) a bank might offer on a 36-month auto loan for various FICO scores.

a. Draw a scatter diagram of the data treating credit score as the explanatory variable.

Verified step by step guidance

1. Step 1: Identify the variables for the scatter diagram. Here, the explanatory variable (independent variable) is the Credit Score, denoted as \(x\), and the response variable (dependent variable) is the Interest Rate (percent), denoted as \(y\).
2. Step 2: Set up the coordinate axes for the scatter plot. Label the horizontal axis (x-axis) as 'Credit Score' and the vertical axis (y-axis) as 'Interest Rate (percent)'. Choose an appropriate scale for each axis to cover the range of the data: Credit Scores from 545 to 750, and Interest Rates from about 5% to 19%.
3. Step 3: Plot each data point on the graph by pairing each credit score \(x\) with its corresponding interest rate \(y\). For example, plot the point \((545, 18.982)\), then \((595, 17.967)\), and so on for all six data points.
4. Step 4: After plotting all points, observe the overall pattern or trend in the scatter diagram. This will help in understanding the relationship between credit score and interest rate.
5. Step 5: Optionally, you can draw a smooth curve or line that best fits the data points to visualize the trend, which in this case is expected to be a decreasing relationship between credit score and interest rate.

Key Concepts

Scatter Diagram

A scatter diagram is a graphical representation that displays the relationship between two quantitative variables. Each point on the plot corresponds to one observation, with the explanatory variable on the x-axis and the response variable on the y-axis. It helps visualize patterns, trends, or correlations between variables.

Explanatory and Response Variables

In a bivariate analysis, the explanatory variable (independent variable) is the one that is presumed to influence or predict changes in the response variable (dependent variable). Here, the credit score is the explanatory variable, and the interest rate is the response variable, as the interest rate depends on the credit score.

Relationship Between Variables

Understanding the relationship between variables involves identifying whether they have a positive, negative, or no correlation. In this case, as credit scores increase, interest rates tend to decrease, indicating a negative correlation. Recognizing this helps in interpreting the scatter plot and further statistical analysis.