To measure the efforts of high-priced public and private colleges and universities to create more economically diverse student bodies, the NY Times calculated a College Access Index, based on the percentage of freshmen in recent years who came from low-income families (measured by the share receiving a Pell grant) and on the net price of attendance for low-income and middle-income families.

The data is in this College Access Index II Excel file.

The variables in the above Excel file used by the NY Times to calculate the College Access Index are as follows:

- Pell (2012 - 2016) is the average percentage of the freshman class that received a Pell grant in 2012-13, 2013-14, 2014-15, and 2015-16, multiplied by the 5-year graduation rate for recent Pell recipients.

- Net price low-to-middle income is the average total cost of attendance in 2015-16, including tuition, fees, room and board, after taking into account federal, state and institutional financial aid, for students who come from households earning between $48,000 and $75,000 a year and qualifying for federal aid.

- Endowment per student is for the year 2012-13 and includes graduate students.

- The College Access Index is a combination of i) net price and ii) a college's Pell graduates, compared with the average school.

A college with an average score on the two measures in combination has a College Access Index of one. Scores above one indicate more access.

Question 1. Using the College Access Index as the explanatory variable and Net price, low-to-middle income as the response variable,
find the slope and intercept of the least squares line. slope of least squares line

Question 2. What is the approximate residual for Duke?