Linear regression Definition and 118 Threads

Consider this situation. There is an exam designed in such a way that it appears that the pass/failure rate of the exam has a linear relationship to the age of the exam taker. The older the test taker, the higher the pass rate. I'm not interested in the exact scores of the exam, only pass or...

Simple linear regression: Y = β0 + β1 *X + ε , where ε is random error Fitted (predicted) value of Y for each X is: ^ Y = b0 + b1 *X (e.g. Y hat = 7.2 + 2.6 X) Consider ^ X = b0' + b1' *Y [the b0,b1,b0', and b1' are least-square estimates of the β's] Prove whether or not...

1) "Simple linear regression model: Y = β0 + β1X + ε E(Y) = β0 + β1X A linear model means that it is linear in β's, and not necessarily a linear function of X. The independent variable X could be W2 or ln(W), and so on, for some other independent variable W." I have some trouble...

1) "Simple linear regression model: Yi = β0 + β1Xi + εi , i=1,...,n where n is the number of data points, εi is random error We want to estimate β0 and β1 based on our observed data. The estimates of β0 and β1 are denoted by b0 and b1, respectively." I don't understand the difference...

1) "In regression models, there are two types of variables: X = independent variable Y = dependent variable Y is modeled as random. X is sometimes modeled as random and sometimes it has fixed value for each observation." I don't understand the meaning of the last line. When is X random...

Homework Statement I've been given a set of data x 0 0.5 0.7 1.5 1.75 y 0.5 0.72 0.51 1.5 1.63 Given y=ax+b for this data points of linear model, I have to 1. minimize the sum of the absolute values of deviations between experimental value of Y and value predicted by the...

Homework Statement Consider model of linear regression: Y_i = \beta_0 + x_i \beta_1 + \epsilon_i i = 1, ..., 5, where \epsilon_i \sim \mathcal{N}(0, \sigma^2) are independent. Find expected value and variance of predicted values \widehat{Y}_i considering that observations are...

I'm interested in fitting a line to some data. There is a built-in function in R lm() that gives me both the best-fit slope and intercept, however, I would like to determine the best fit intercept GIVEN a specified value of the slope. Is there an easy way to do this? I apologize if this is in...

AFAIK, there are two basic type of linear regression: y=ax+b and y=a2 + bx + c But I have to do the same with the function y = asin(x)+bcos(x). Here is what I have done: We have: \begin{array}{l} \frac{{\partial L}}{{\partial a}} = 0 \frac{{\partial L}}{{\partial b}} = 0Continue...

[SOLVED] Multivariate Linear Regression With Coefficient Constraint I'm attempting a multivariate linear regression (mvlr) by method of least squares. Basically, I'm solving a matrix of the following form for \beta_p, $ \begin{bmatrix} \sum y \\ \sum x_1 y \\ \sum x_2 y \\ \sum x_3 y...

For my chemistry lab, in order to computer change in temperature for a calorimetry experiment we're suggested to take the line of best fit from the peak temperature onwards (excluding the initial data) and extrapolate to y = 0. For example, here's some of the data I gathered: A, Trial 2...

1) To test the quality of a tennis ball you drop it onto the floor from a hieght of 4 m. it rebounds to a hieght of 2 m. if the ball is in contact with the floor for 12 ms, what is the magnitude of its average acceleration during contact and is the average acceleration up or down. What i did...

My problem in short: I have a set of data, and I want to calculate the linear regression, and the uncertainty of the slope of the linear regression line, based on the uncertainties of the variables My problem in detail: My data is from an experiment and the uncertainties (errors) are...

Hi, I've got what should be a very easy simple linear regression problem, but I can't seem to be able to get my head around it. Here it is: So far I've been trying to sub these values into a regression equation like this one: Y = 5B + (-0.003)B^2 Where "B" is my Beta1 value. I...

linear regression where am i going wrong?? Linear regression using least square fit method for the determination of cocaine sample Cocaine (mg/ml) Peak height X= 2.75 Y=27377 X squared=0.9625 X x Y=3241.272 M = 10 x 3241.272 – 2.75 x 27377 / 10 x 0.9625 – 7.5625 =...

Im having some trouble with this, and I was hoping someone could help me. I have a data set from which I've determined the \widehat{a} and \widehat{b} values and determined where the line of best fit should go using linear regression. The next thing I have to do is work out the varience using...

It seems to me that Linear Regression and Linear Least Squares are often used interchangeably, but I believe there to be subtle differences between the two. From what I can tell (for simplicity let's assume the uncertainity is in y only), Linear Regression refers to the general case of fitting...

Hi, Complicated stats question, but maybe someone out there knows how to proceed. I am trying to perform regression on two variables, the samples of which have significant, but known error components. Ordinary least squares regression cannot be used as it is assumed that measurements are made...