Regression line Definition and 15 Threads

I analyzed the relationship between the surface temperature and luminosity of stars of similar mass using a regression model. Through this, I was able to obtain a regression line. Since stars of similar mass show similar evolutionary paths, I believe this regression line can be viewed as a rough...

Hello, I was considering some made up data ##(X,Y)## and a its best fit regression line. The outcome variable ##Y## is the number of likes and ##X## is the number of comments on a website. We have 100 data points which spread in such a way that the best fit line has zero slope. This implies...

The question is as shown below. ( Text book question). The textbook solution is indicated below. Discussion; Now they seemingly used ##r=1## to arrive at ##x=0.8+0.2y##. That is, ##y=-4+5x## then, since ##r=1##, ...implying perfect correlation therefore, ##5x=4+y## ##x=0.8+0.2y## My other...

I have note that states regression line x on y is used when we want to calculate x for given y but in this case y is dependent variable. I am pretty sure I can use either line if the value of product moment correlation coefficient (r) is close to 1 but for the case, let say r = 0.6, can we use...

Hi! Basically this is the exercise: Given the covariance of x and y is -12 and the variance of x is 6,5, using the least squares line of best fit connecting x and y yo estimate the value of x when y=15 x 2 5 9 7 9 10 7 y 25 17 11 10 8 7 13 any help would mean everything, I'm desperate :(

Homework Statement I am trying to perform a weighted fit of a data set ##(x,y)## shown below. The only information I have are the two vectors ##x## and ##y## and the uncertainty present in the ##y## values (##=0.001##). Homework Equations The Attempt at a Solution Statistical weighting of...

Homework Statement A random sample of size ##n## from a bivariate distribution is denoted by ##(x_r,y_r), r=1,2,3,...,n##. Show that if the regression line of ##y## on ##x## passes through the origin of its scatter diagram then[/B] $$\bar y \sum^n_{r=1} x_r^2=\bar x\sum^n_{r=1} x_r y_r$$ where...

The slope of a fitted line = Cov(X,Y)/Var(X). I've seen the derivation of this, and it is pretty straightforward, but I am still having trouble getting an intuitive grasp. The formula is extremely suggestive and it is bothering me that I can't quite see its significance. Perhaps, my mental...

Homework Statement I'm being asked to compare the standard deviation of a data set with the root mean square error of the regression line used to model the data, in order to determine the reliability of the regression line. Homework Equations Mean squared error = variance + bias squared The...

I have set of date with error bars of different length on my y values. I want to know what the error is on the slope and intercept of my line of best fit through this data. Is there a numerical way to calculate this that takes into account the fit of the regression line and the y error bars?

I'm currently trying to determine the error on the slope of a regression line and the y-intercept. My y values are: My y error is: My x values are: 27.44535013 0.03928063 136 29.78207524 0.07836946 44 27.4482858 0.0385213 143 27.27481069...

urgent reply needed Can we use partial means as a predictor for the response while fitting a regression line or curve?.

Homework Statement I'm new to uncertainty, so I needed a little assistance. The circuit in this experiment was simple, a dry cell connected to a variable resistor. I used an ammeter on the circuit and used a voltmeter across the resistor and took some measurments. The experiment was to...

i need to calculate the closest distance of the point that lies closest to the regression line for my programing but i am not sure what is the formula. maybe someone can help me out here? thanks in advance

OK, I have a question I have no idea how to answer (and all my awful undergrad stats books are useless on the matter). Say I make a number of pairs of measurements (x,y). I plot the data, and it looks strongly positively correlated. I do a linear regression and get an equation for a line of best...