Final answer:
To analyze professors' monthly salaries as a function of years since earning a PhD, the student should construct a scatter diagram, look for patterns, consider the significance of the y-intercept, calculate the least-squares line, and compute the correlation coefficient.
Step-by-step explanation:
The student's question is about constructing a scatter diagram to analyze the relationship between the monthly salary (Y) of professors and the number of years since being awarded a PhD (T). To address this, follow these steps:
Plot the data points in a graph with the monthly salary (Y) on the vertical axis and the number of years since being awarded a PhD (T) on the horizontal axis.
Upon inspecting the scatter diagram, determine if there appears to be a relationship between the two variables. Look for any visible pattern or trend in how the data points are distributed.
Analyze whether the y-intercept, represented as 'a' in the equation ŷ = a + bx, holds any significance for the interpretation of the data in the context of the study.
Calculate the least-squares line to find the best-fitting line for the data, which will have the form ŷ = a + bx.
Compute the correlation coefficient to assess the strength and direction of the relationship between monthly salary and years since PhD, and determine if it is statistically significant.
These steps will help the researcher to visualize the data and conduct a preliminary analysis to understand the potential relationship between years since receiving a PhD and professor salaries.