I'm attempting to calculate p-values and t-statistics for multiple regression, but all the resources I've been finding on the topic have confusing or inconsistent information. The best resource I've been able to find is this one (https://online.stat.psu.edu/stat501/lesson/2/2.12) which has helped me understand that t-statistics for each coefficient are the coefficient divided by the SE, but there are still many aspects I'm unsure on. Namely, the page mentions that Standard Error (SE) is "a measure of [each statistic's] accuracy", but doesn't go into further detail beyond that. I've heard that Standard Error is the same thing as the Root Mean Square Error (RMSE), but I keep getting conflicting information on whether that's true or not. Furthermore, the page mentions that the p-value is the area underneath the t distribution for the portion beyond -t and +t, but doesn't elaborate on what the formula would be to calculate it.
The values I'm current able to calculate for the regression are the R2, gradient, y-intercept, and the RMSE. I also obviously have my dependent variables and n amount of independent variables.
Are the Root Mean Square Error and the Standard Error the same thing? If not, how should I go about calculating the Standard Error for each coefficient?
Given that the p-value is the area under the curve of the t distribution beyond the positive and negative t boundaries, what is the formula I should be using to calculate it?
Can p-values, t-statistics, and Standard Error be calculated for the entire formula? Or can they only be calculated for each coefficient individually?
Apologies if the information I've given here is hard to follow - I'm very confused about this topic myself, and have spent days trying to wrap my head around it with very little to show for it.