Thank you for uploading the Unit 2 and Unit 3 videos so quickly! We really appreciate your immediate response and commitment to helping us prepare for our midterm exams. Your efforts are truly appreciated, and your explanations are excellent!
🎯 Key Takeaways for quick navigation: Linear regression analyzes the relationship between variables to predict unknown values. Regression analysis involves an independent variable predicting a dependent variable based on data. Linear regression uses a straight line as the curve of regression if the relationship is linear. The principle of least squares minimizes the distance between the regression line and data points. Normal equations help find regression coefficients A and B. Regression lines can be of Y on X or X on Y, depending on the scenario. The regression line of Y on X passes through the point (X bar, Y bar) where X bar is the mean of X and Y bar is the mean of Y. Similarly, the regression line of X on Y also passes through the point (X bar, Y bar). Two regression lines are often needed because they minimize different distances (perpendicular vs. horizontal). Regression lines intersect at the point (X bar, Y bar). Calculations involve summations of X, Y, X square, Y square, and X times Y to find regression coefficients. Solving normal equations helps determine the regression lines. At timestamp - 22:35, the regression line equations for X on Y and Y on X are derived. Solving the regression line equations yields the mean values of X and Y (- 26:20). Regression coefficients are independent of a change of origin but not of scale (- 36:18). The angle between two regression lines can be calculated using the tangent of the difference in slopes (- 38:34). The angle θ in linear regression is determined by tan inverse(1/R), where R is the correlation coefficient. When R = 0, indicating no correlation, the regression lines are perpendicular. When R = ±1, indicating perfect correlation, the regression lines coincide or are parallel. Regression coefficients are independent of origin changes but not of scale changes. Changing the origin for calculation purposes simplifies regression coefficient determination. Calculations involve finding covariance, variance, and deviation from the mean. Regression equations can be solved to find mean values for X and Y. The correlation coefficient between X and Y is the geometric mean of the two regression coefficients. 01:07:18 *Regression lines of Y on X and X on Y are calculated using their respective equations.* 01:10:41 *Correlation coefficient (R) is calculated as 0.6 for the given regression coefficients, ensuring they have the same sign.* 01:11:59 *Standard deviation of Y (Sigma Y) is determined using the regression coefficient and known values.* 01:13:12 *Using regression equations, the most likely price in Mumbai corresponding to a given price in Kolkata is calculated.* 01:14:56 *The provided equations cannot represent regression, as the regression coefficient for Y on X must be positive and for X on Y must be negative.* Made with HARPA AIf
1:12:40 sir if we change the equations X on Y and Y on X, then r will inverse from your answer (r=5/3). but sigma y remain same... Sir my doubt is that if we change equations according to X on Y and Y on X then correlation coifficient will also change. So which one is correct...🤔
Sir please upload mcq's of unit 1,2 and 3 as we have exam on 20th September, please sir upload fast by today just seeing videos will not help us sir if you send mcqs we would top in the exams beacuse of you!!!! 🥺🥺
sir i just took over view of this whole playlist sir is this enough for machine learning mathematics at least basics? or if possible sir can you suggest me books for question practice.
Thank you for uploading the Unit 2 and Unit 3 videos so quickly! We really appreciate your immediate response and commitment to helping us prepare for our midterm exams. Your efforts are truly appreciated, and your explanations are excellent!
🎯 Key Takeaways for quick navigation:
Linear regression analyzes the relationship between variables to predict unknown values.
Regression analysis involves an independent variable predicting a dependent variable based on data.
Linear regression uses a straight line as the curve of regression if the relationship is linear.
The principle of least squares minimizes the distance between the regression line and data points.
Normal equations help find regression coefficients A and B.
Regression lines can be of Y on X or X on Y, depending on the scenario.
The regression line of Y on X passes through the point (X bar, Y bar) where X bar is the mean of X and Y bar is the mean of Y.
Similarly, the regression line of X on Y also passes through the point (X bar, Y bar).
Two regression lines are often needed because they minimize different distances (perpendicular vs. horizontal).
Regression lines intersect at the point (X bar, Y bar).
Calculations involve summations of X, Y, X square, Y square, and X times Y to find regression coefficients.
Solving normal equations helps determine the regression lines.
At timestamp - 22:35, the regression line equations for X on Y and Y on X are derived.
Solving the regression line equations yields the mean values of X and Y (- 26:20).
Regression coefficients are independent of a change of origin but not of scale (- 36:18).
The angle between two regression lines can be calculated using the tangent of the difference in slopes (- 38:34).
The angle θ in linear regression is determined by tan inverse(1/R), where R is the correlation coefficient.
When R = 0, indicating no correlation, the regression lines are perpendicular.
When R = ±1, indicating perfect correlation, the regression lines coincide or are parallel.
Regression coefficients are independent of origin changes but not of scale changes.
Changing the origin for calculation purposes simplifies regression coefficient determination.
Calculations involve finding covariance, variance, and deviation from the mean.
Regression equations can be solved to find mean values for X and Y.
The correlation coefficient between X and Y is the geometric mean of the two regression coefficients.
01:07:18 *Regression lines of Y on X and X on Y are calculated using their respective equations.*
01:10:41 *Correlation coefficient (R) is calculated as 0.6 for the given regression coefficients, ensuring they have the same sign.*
01:11:59 *Standard deviation of Y (Sigma Y) is determined using the regression coefficient and known values.*
01:13:12 *Using regression equations, the most likely price in Mumbai corresponding to a given price in Kolkata is calculated.*
01:14:56 *The provided equations cannot represent regression, as the regression coefficient for Y on X must be positive and for X on Y must be negative.*
Made with HARPA AIf
Very good
Sir jub aap welcome everyone bolte hona . Mast lagta hai sir ek baar aap theater ya movie try karo
thank you so much sir
please complete unit 3 also sir
if you wi;; change the regression of y on x to regression of x on y then, the product of bxy * byx will be greater than 1 which should be there.
1:12:57 if we change x on y and y on x the value of r goes beyond its range
Sir, but for 1:15:58 question the tan(theta) says that the lines exist with tan(theta)=8 somewhere btw 60° and 90°. Please try to explain.
Both are equations of line.We need to check whether they are regression lines?
@@Sanonlineclasses I totally missed that point, Dhanyavad Sir .
1:12:40 sir if we change the equations X on Y and Y on X, then r will inverse from your answer (r=5/3). but sigma y remain same... Sir my doubt is that if we change equations according to X on Y and Y on X then correlation coifficient will also change. So which one is correct...🤔
Idea is regression coefficients and correlation coefficient should be of same sign,also correlation coefficient should lie between -1to 1
Got it, sir 👍
sir, why u chose first one as regression line on y on x...i didn.t understood please tell
if you wi;; change the regression of y on x to regression of x on y then, the product of bxy * byx will be greater than 1 which should be there.
Sir please upload mcq's of unit 1,2 and 3 as we have exam on 20th September, please sir upload fast by today just seeing videos will not help us sir if you send mcqs we would top in the exams beacuse of you!!!! 🥺🥺
Sir how did you consider the regression line as y on x and x on y at 1:7:12
if considered other way around the r value is 1.66 which is not possible.
sir i just took over view of this whole playlist sir is this enough for machine learning mathematics at least basics? or if possible sir can you suggest me books for question practice.
Let me check ,what is the requirements for ML.I will respond accordingly.
sure sir.
Sir, have you checked ??
yes up to a certain extent it covers @@liveforkillarpit
Thanks sir ji🙏🙏
Thank you sir
So nice of you
thank you sir
hindi is more comfortable sir as compare of english
This video is very boring
Watching with 1.5x may help.
Thank you sir