What is an adjusted R-Squared Statistics?

Scientists observed that as the number of independent variables increased, so did the value of R-Squared Statistics. Thus casting doubt on the reliability of R-Squared Statistic. To remedy this vulnerability adjusted R-Squared Statistics was introduced. Its equation penalizes/counters the increase in R-Squared Statistics with increase in number of variables by introducing number of columns in the denominator of R-Squared calculations.

What is gradient descent, and why is it used?

Gradient descent equation describes relationship between (1) current value of error and next value of error, or (2) slope (say m) and intercept of regression line (say c) and the corresponding error.

The error term is differentiated (partial derivatives) with respect to m & c. Then the resultant equations (1st order derivative) is equated with zero, as at minima the value of first order derivative is zero, and the values of m & c are calculated to plot/get the best fit line.