Calculate standard error based on ssr and sst

If we reject the null hypothesis, we conclude that there is at least one significant variable in other words, we have enough evidence to conclude that at least one X variable explains variation in the Y variation. The F-statistic, F = MSR/MSE, is relevant for testing the null hypothesis that all of the population slope coefficients are equal to zero against the alternative that at least one of the population slope coefficients is not equal to zero: MSE is mean squared error, and equals SSE/DFE. MSR is the mean squared regrssion, and equals SSR/DFR. The degrees of freedom for SSR are labeled DFR and equal p. The degrees of freedom for SSE are labeled DFE and equals N - p - 1.

The degrees of freedom for SST are labeled DFT, and equals N-1. With some algebra, we could show that SST = SSE + SSR. The analysis of variance (ANOVA) table summarizes several quantities associated with the regression equation: If we assume that the random variable РћВµ has a normal distribution, then the estimate has a normal distribution with a mean of РћР† and variance equal to. The estimate is unbiased, which means that, on average, the estimate will equal the population value. Then the least squares estimates of the coefficients are given by. we can write the vector of population coefficients as. We can write the set of X variables in matrix form, where 1 is an Nx1 vector of ones. The random variable РћВµ has a normal distribution with a variance, РџС“ 2, that is constantР”Р„s in simple regression, the parameters of the regression model are estimated by finding values, that minimize the sum of squared errors.In order to conduct inference in the multiple regression model, we often make an additional assumption: The random variable РћВµ has a mean of zero and is uncorrelated with the X variables.The data is a random sample from the population.We will use the sample to estimate the parameters of the population regression model. Suppose we have a random sample of N observations from the population:, i = 1.,N. The term РћВµ is a random variable that has mean zero and is uncorrelated with the independent variables. The Y variable is sometimes called the response variable, while the X's are sometimes referred to as the predictor variables. Multiple regression refers to a model in which a dependent variable, Y, is a linear function of a set of independent variables, X 1, X 2. The goal of multiple regression is to develop a linear model that can be used to explain variation in the Y variable or to predict values of the Y variable.

Calculate standard error based on ssr and sst