Is Mse Still Reliable

How do you find the MSE of interaction from a factorial ANOVA output? I am aware that it is often presented in the interaction's error row, however only an error row exists for one of the interactions, rather than all of them.

I’m going to assume you have a factorial design with a number, say k, of fixed factors. You’ve also got a response variable. You’ve got [math]2^k[/math] rows of data.The anova table could be written a with:One row for each main effect, k of these rowsOne row for each 2-way interaction, k(k-1)/2 of these rowsOne row for each 3-way interaction, k(k-1)(k-2)/6 of these rowsEtc. Until…One row for the k-way interaction, one of these rows.Each row has one degree of freedom and there are [math]2^k-1[/math] rows in your anova table. There are no degrees of freedom left for the error. We have to get around this problem.We usually combine all higher order interactions and let them become the error. If k is large, we usually combine all interactions higher than 2-way. If k is small, we combine all interactions, and only keep the main effects. This is ok since higher order interactions are often not significant, and so they’re variability is nothing more than random error.To combine interactions and thus create the error row of the anova table, simply add the appropriate interaction sums of squares and call this sum the error sum of squares. Similarly add the appropriate interaction degrees of freedom and call this sum the error degrees of freedom. Then divide to make a MSE.

Are the free anti-virus programs like MSE or McAfee essential for Windows 8?

First of all it is highly recommended that one should always have a Anti-virus software, either paid or free, in their computer system. To further explain this:Let's break this in two parts. I'm going to broadly classify computer users in two categories. First, there are basic users who uses their personal computers for daily use like surfing, shopping and downloading. For such kind of users it is recommended that they must use either paid or at least should have a basic free version of antivrus software installed in their computer. Since majority of the threats comes from the internet and the removable flash drives, it is thus indeed necessary even for a basic user to have an antivirus program on their PC.Second, the POWER USERS who uses their PC for virtually everything which a basic users do plus some highly sensitive work like Internet banking, business related transaction etc. Such kind of users are the main target of hackers and viruses. For such users it is highly recommended to use a paid antivirus system which provide not only basic threat protection but also support some high security features like Firewall, LinkScanner, Rootkit scanner etc.  Although no antivirus guarantee you 100% protection but still "Prevention is better than cure."

Why is mean square error used instead of cross entropy, for linear regression loss function?

In machine learning,The (mean) cross entropy is a measure of difference between two discrete probability distributions. In particular the categorical cross entropy is used as the loss function where the target variable is binary (0, 1) with some probability (0..1).The mean squared error is a measure of distance (expressed as the variance) between two sets of real (continuous) values (-inf .. +inf).Linear regression is used as the estimator of a continuous target variable and hence the MSE is used.

Is Microsoft security essentials or Windows Defender really a good anti-virus programme?

Sure; Why not? It is offered by Microsoft with windows 10 ; it means, it is capable to protect your PC.But if you think that you download Games, third party software, video, audio and such other work activities then you can install a premium version of antivirus like Norton, McAfee, bitdefender, vipre and other to protect fully your PC.If you use your PC normally to surfing internet then Windows defender is enough for you. So don’t worry about anythings.Thanks .. If you have other question don’t hesitate to ask..

What is the difference between squared error and absolute error?

Say you define your error as,[math]Predicted Value - Actual Value[/math]. Then the error in estimation can be of two kinds,You underestimate the value, in which case your error will be negative.You overestimate the value, in which case your error will be positive.When you average these out, you might get a very low error if you are underestimating and overestimating equally as they will cancel each other out. To get rid of the effect of the negative value while taking the mean, we square them.A better question would be why not use the absolute difference instead of squaring the errors. This has no definite answer as it is very application specific. In cases where you want to emphasize the spread of your errors, basically you want to penalize the errors that are farther away from the mean (usually 0 in machine learning, a user parameter in statistics). In small scales where your errors are less than 1 because the values themselves are small, taking just the absolute might not give the best feedback mechanism to the algorithm.Though the above statement cannot be used everywhere, you have to carefully consider your problem and then decide. Sometimes you want your error to be in the same units as your data. In which case, you individually square the error for each observation and take the square root of the mean. This lets you factor for more spread as well as keeping the units constant.TL;DR: Squared for getting rid of the negative errors affecting the mean. Both absolute values and squared values are used based on the use-case.