Linear Regression Equation Explained Here

If the coefficients of a simple regression line, $B_{0}$ and $B_{1}$ , are the same then why are the regression lines of $y$ on $x$ and $x$ on $y$ different given the condition $r^{2} < 1$ . I have tried all the manipulation and graphical analysis I can but can't seem to see why this is happening.

Jeramiah Campos 2022-06-29

Show how the nonlinear regression equation $y = a X^{B}$ can be converted to a linear regression equation solvable by the method of least squares.

Mara Cook 2022-06-25

While doing the analysis, I did a simple regression and check out that some variables have low p-value. Therefore I thought they are influential variables for dependent variable.
So I did Multiple regression with influential variables, but p-values become not influentially low and less significant (less descriptive). Is this case some kind of multicolinearity? I've heard a lot about the opposite result (the more variable added, the insignificant variable becomes more descriptive), but I'm not sure about this case.

Reginald Delacruz 2022-06-24

Let a sample $(x, y) \in R^{2 n}$ be given, where $y$ only attains the values $0$ and $1$ . We can try to model this data set by either linear regression
$y_{i} = α_{0} + β_{0} x_{i}$
with the coefficients determined by the method of least squares or by logistic regression
$π_{i} = \frac{\exp (α_{1} + β_{1} x_{i})}{1 + \exp (α_{1} + β_{1} x_{i})},$
where $π_{i}$ denotes the probability that $y_{i} = 1$ under the given value $x_{i}$ and the coefficients are determined by the Maximum-Likelihood method. My question is whether the following statement holds true.
Claim: If $β_{0} > 0$ ( $β_{0} < 0$ ), then $β_{1} > 0$ ( $β_{1} > 0$ ).
I figure this could be due to the sign of the correlation coefficient.

polivijuye 2022-06-22

Specific equations for the three parameters in a least-squares quadratic regression? I'm looking for something like $β_{1} =, β_{2} =, β_{3} =$ for each of $y = β_{1} + β_{2} x + β_{3} x^{2}$ . To be clear, the right side of each of these equations should be evaluateable, using the data, to find the parameter.

Poftethef9t 2022-06-21

Given $X$ and $Y$ sample data as something like
$[\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}]$
$[\begin{matrix} 7 \\ 8 \end{matrix}]$
In such an arrangement how do I include B3? I would think I would want to add it in as always 1 in $X$ . IE
$[\begin{matrix} 1 & 2 \\ 2 & 3 \\ 1 & 1 \end{matrix}]$

misurrosne 2022-06-15

regression $x (t) = a t + b$ , number of trials, and $R_{2}$ of the regression. How do I find the value and $95 %$ confidence interval for the value of $V = x / t$ ?

manierato5h 2022-06-15

Let's say we have two random variables $Y$ and $X$ used to form regression model
$Y = α + β X + μ$
It also holds that $E (μ) = 0$ , $Var (μ) = σ_{μ}^{2}$ , $Var (X) = σ_{X}^{2}$ , $Var (Y) = σ_{Y}^{2}$ , $Corr (X, Y) = r$ and $Corr (X, μ) = r_{X μ}$ . Find $β$ . I tried to solve this as follows:
For simple linear regression $β = \frac{Cov (X, Y)}{Var (X)}$ and $Corr (X, Y) = \frac{Cov (X, Y)}{σ_{X} σ_{Y}} = r$ so that:
$β = \frac{Corr (X, Y) \cdot σ_{X} σ_{Y}}{σ_{X}^{2}} = r \frac{σ_{Y}}{σ_{X}}$
Is this as simple as this?

Damon Stokes 2022-06-10

We have to determine the effect of a predictor variable on an outcome variable using simple linear regression. We have lots of data (about 300 variables) and we may include some other covariates in our regression model. Why would we include other covariates and how do you decide which of those 300 variables we want to include in our regression model?

shmilybaby4i 2022-06-09

Help to understand
$e_{i} = y_{i} - a x_{i} - b$
$e_{i} = (y_{i} - \bar{y}) - a (x_{i} - \bar{x}) - (b - \bar{y} + a \bar{x})$

Paul Webster 2022-06-04

Short version, I need to find a regression to this: $a \equiv t (\mod Δ)$ , $a$ and $Δ$ are the unknowns constants.
Any idea where I should start looking?
Some context, because I may be wording it in a confusing way: I am trying to find the tempo of time-stamped events $t_{i}$ for some real time musical analysis. They have a typical interval of $Δ$ , but there isn't an event at every "tick", so no linear regression, and there may be more than one event for a given "tick". In other words, $t_{n + 1} - t_{n}$ may be $0$ or any $m Δ$ .

Paul Webster 2022-06-04

Short version, I need to find a regression to this: $a \equiv t (\mod Δ)$ , $a$ and $Δ$ are the unknowns constants.
Any idea where I should start looking?
Some context, because I may be wording it in a confusing way: I am trying to find the tempo of time-stamped events $t_{i}$ for some real time musical analysis. They have a typical interval of $Δ$ , but there isn't an event at every "tick", so no linear regression, and there may be more than one event for a given "tick". In other words, $t_{n + 1} - t_{n}$ may be $0$ or any $m Δ$ .

Chandini Pamulapati2022-06-03

Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis of these data, we may conclude that the mean systolic blood pressure for a population of African-American is greater than 140.
- Setup the null and alternate hypothesis
- Determine the type of the test
- Use a=0.01, conduct the test and accept or reject the hypothesis on the basis of the test.

Jornelecrearlqx2un 2022-06-02

If the joint density function of $X$ and $Y$ is given by:
$f (x, y) = {\begin{cases} 1 / 2, & for | x | + | y | \leq 1 \\ 0, & otherwise \end{cases}$
Show that $Y$ has constant regression with respect to $X$ and/but that $X$ and $Y$ are not independant.

dokezwa17 2022-05-28

A similarity/metric learning method that takes in the form of $x^{T} W y = z$ , where $x$ and $y$ are real valued vectors. For example, two images.
Breaking it into a more familiar form:
$x^{T} W y = \sum_{i j} w_{i j} x_{i} y_{j} = z$
This essentially looks very similar to polynomial regression with only interactions between features (without the polynomials). i.e.
$z = f_{w} (x) = \sum_{i} w_{i} x_{i} + \sum_{i} \sum_{j = i + 1} w_{i j} x_{i} x_{j}$
I was curious to see if the optimization for the matrix $W$ is the same as doing optimization for multivariate linear/polynomial regression, since $x$ and $y$ are fixed, and the only variate is the weight matrix $W$ ?

Mackenzie Rios 2022-05-24

Is there a method for polynomial regression in $2 D$ dimensions (fitting a function $f (x, y)$ to a set of data $X, Y$ , and $Z$ )? And is there a way to apply a condition to the regression in $2 D$ that requires all functions fitted to go through the axis line $x = 0$ ?

agdv9m 2022-05-24

set $S$ of coordinates $(x, y)$ , and am estimating $f (x) = a x + b$ where $a > 0$ . I also happen to know that $\forall x, y ((x, y) \in S ⟹ y < f (x))$ .
The question is how I can utilize this knowledge of the upper bound on values to improve the regression result?
My intuition is to run a "normal" linear regression on all coordinates in $S$ giving $g (x)$ and then construct $g^{'} (x) = g (x) + c$ , with $c$ being the lowest number such that $\forall x, y ((x, y) \in S ⟹ y \leq g^{'} (x))$ , e.g. such that $g^{'} (x)$ lies as high as it can whilst still touching at least point in $S$ . I do, however, have absolutely no idea if this is the best way to do it, nor how to devise an algorithm that does this efficiently.

Rachel Villa 2022-05-23

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
$\bar{y} \sum_{r = 1}^{n} x_{r}^{2} = \bar{x} \sum_{r = 1}^{n} x_{r} y_{r}$
where $(\bar{x}, \bar{y})$ is the mean point of the sample.

ga2t1a2dan1oj 2022-05-08

$X =$ Lot & $Y =$ Cost
Give a broken line linear model with a breakpoint at $250$ :
$Y = B_{0} + B_{1} X_{1} + B_{2} X_{2} + B_{3} X_{3} + e$
where $X_{2} = 0$ or $1$ depending on whether the lot size is $\geq 250$ or $< 250$ and $X_{3} = X_{1} \cdot X_{2} .$ .
Which hypothesis statement is equivalent to the statement: The two regression lines have the same intercept term?
$H_{0} : B_{0} = 0 H_{0} : B_{1} = 0 H_{0} : B_{2} = 0 H_{0} : B_{3} = 0$
$B_{0}$ is obviously the intercept for simple linear regression models, however, the broken line phrasing is causing me to be confused on this. My initial instinct was to assume $B_{0}$ hypothesis was appropriate, but now I'm wondering if $B_{2} = 0$ makes more sense.

velinariojepvg 2022-05-08

If I have built two linear regression models over sets $A$ and $B$ , and now want a linear regression over set $A \cup B$ .Is there a way to reuse what I already have?

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.

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Expert Help with Regression Line Equation