Linear Regression Equation Explained Here

Is the total sum of squares for multiple regression the same as the total sum of squares for anova?
Is anova a test for bivariate correlation or multiple regression?

Kendall Oneill 2022-05-08

What do you mean by a distribution is homoscedastic (ie, $σ (Y | X = x) = σ$ ) in the context of simple linear regression? Why do we need this assumption in simple linear regression? What will happen to the regession if a distribution is not homoscedastic?

Carley Haley 2022-05-08

In Linear regression, we have $θ = {(X^{T} X)}^{- 1} X^{T} y$ .
In Ridge regression, we have $θ = {(λ I + X^{T} X)}^{- 1} X^{T} y$ .
I learnt somewhere that while $X^{T} X$ is not guaranteed to be invertible, $λ I + X^{T} X$ is guaranteed to be invertible.
Is this true? If so, why?

Porter Mccullough 2022-05-03

Table of values
$\begin{array}{cccccc} x & 1 & 2 & 3 & 4 & 5 \\ y & 3 & 6 & 8 & 9 & 0 \\ y & 4 & 6 & 1 & 2 & 4 \end{array}$
and know that it is a simple linear regression model, what is the value of $n$ ? I think it is either $5$ or $10$ but am not sure which one.

ga2t1a2dan1oj 2022-04-07

We have a situation where we have pairs of points where x=heights of fathers and y=heights of the sons of these fathers. The mean of $X$ is equal to the mean $Y$ and $S D (Y) = S D (X)$ , and $0 < R < 1$ . Now I am supposed to show that the expected height of a son whose father is shorter than avg. is also less than average, but by a smaller degree. First off I need help understanding the "regression effect" i.e. "Regression Towards the Mean." If the standard deviations are the same why is this happening?

An essential part of inferential statistics and studies of probability in engineering, economics, and related disciplines is understanding the regression problems. This concept is often used in machine learning as one needs to predict the quantity of something. It can be either a real value or discrete input variables. See the free suggestions for similar tasks, you may also find questions on multivariate regression challenges that will help you to see how the answers came about. As you take a look through at least one regression equation example, you will understand how prognosis and the concept of probability work together.

Inferential Statistics

Expert Help with Regression Line Equation

Is the total sum of squares for multiple regression the same as the total sum of squares for anova?Is anova a test for bivariate correlation or multiple regression?

What do you mean by a distribution is homoscedastic (ie, σ ( Y | X = x ) = σ) in the context of simple linear regression? Why do we need this assumption in simple linear regression? What will happen to the regession if a distribution is not homoscedastic?

In Linear regression, we have θ = ( X T X ) − 1 X T y .In Ridge regression, we have θ = ( λ I + X T X ) − 1 X T y .I learnt somewhere that while X T X is not guaranteed to be invertible, λ I + X T X is guaranteed to be invertible.Is this true? If so, why?

Table of values x 1 2 3 4 5 y 3 6 8 9 0 y 4 6 1 2 4 and know that it is a simple linear regression model, what is the value of n? I think it is either 5 or 10 but am not sure which one.

Is the total sum of squares for multiple regression the same as the total sum of squares for anova?
Is anova a test for bivariate correlation or multiple regression?

What do you mean by a distribution is homoscedastic (ie, $σ (Y | X = x) = σ$ ) in the context of simple linear regression? Why do we need this assumption in simple linear regression? What will happen to the regession if a distribution is not homoscedastic?

In Linear regression, we have $θ = {(X^{T} X)}^{- 1} X^{T} y$ .
In Ridge regression, we have $θ = {(λ I + X^{T} X)}^{- 1} X^{T} y$ .
I learnt somewhere that while $X^{T} X$ is not guaranteed to be invertible, $λ I + X^{T} X$ is guaranteed to be invertible.
Is this true? If so, why?

Table of values
$\begin{array}{cccccc} x & 1 & 2 & 3 & 4 & 5 \\ y & 3 & 6 & 8 & 9 & 0 \\ y & 4 & 6 & 1 & 2 & 4 \end{array}$
and know that it is a simple linear regression model, what is the value of $n$ ? I think it is either $5$ or $10$ but am not sure which one.