What is a standardized regression coefficient?

Lorena Lester
2022-07-18
Answered

What is a standardized regression coefficient?

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Jaylene Tyler

Answered 2022-07-19
Author has **10** answers

Explanation:

In statistics, standardised coefficients or beta coefficients are the estimates resulting from a regression analysis that have been standardised so that the variances of dependent and independent variables are 1.

Try to understand the advantage of standardised regression coefficients that these ignore the independent variable's scale of units, which makes comparisons easy.

For further information see the link given below

In statistics, standardised coefficients or beta coefficients are the estimates resulting from a regression analysis that have been standardised so that the variances of dependent and independent variables are 1.

Try to understand the advantage of standardised regression coefficients that these ignore the independent variable's scale of units, which makes comparisons easy.

For further information see the link given below

asked 2022-06-24

Let a sample $(x,y)\in {\mathbb{R}}^{2n}$ be given, where $y$ only attains the values $0$ and $1$. We can try to model this data set by either linear regression

${y}_{i}={\alpha}_{0}+{\beta}_{0}{x}_{i}$

with the coefficients determined by the method of least squares or by logistic regression

${\pi}_{i}=\frac{\mathrm{exp}({\alpha}_{1}+{\beta}_{1}{x}_{i})}{1+\mathrm{exp}({\alpha}_{1}+{\beta}_{1}{x}_{i})},$

where ${\pi}_{i}$ 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 ${\beta}_{0}>0$ (${\beta}_{0}<0$), then ${\beta}_{1}>0$ (${\beta}_{1}>0$).

I figure this could be due to the sign of the correlation coefficient.

${y}_{i}={\alpha}_{0}+{\beta}_{0}{x}_{i}$

with the coefficients determined by the method of least squares or by logistic regression

${\pi}_{i}=\frac{\mathrm{exp}({\alpha}_{1}+{\beta}_{1}{x}_{i})}{1+\mathrm{exp}({\alpha}_{1}+{\beta}_{1}{x}_{i})},$

where ${\pi}_{i}$ 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 ${\beta}_{0}>0$ (${\beta}_{0}<0$), then ${\beta}_{1}>0$ (${\beta}_{1}>0$).

I figure this could be due to the sign of the correlation coefficient.

asked 2022-07-22

Correlation and causation data

What are some real life examples (data) in which high correlation:

1) implies causation

2) doesn't imply causation.

I know that there is a lot of data out there of weird correlations, like divorce rate and consuption of margarine, but the problem with this data is, that we don't really know if one is caused by the other, because nobody tested it, so we cannot strictly say that they're unrelated.

What are some real life examples (data) in which high correlation:

1) implies causation

2) doesn't imply causation.

I know that there is a lot of data out there of weird correlations, like divorce rate and consuption of margarine, but the problem with this data is, that we don't really know if one is caused by the other, because nobody tested it, so we cannot strictly say that they're unrelated.

asked 2022-05-08

What do you mean by a distribution is homoscedastic (ie, $\sigma (Y|X=x)=\sigma $) 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?

asked 2022-07-16

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. $r=0.767,n=25$

a. Critical values: $r=\pm 0.396$, no significant linear correlation

b. Critical values: $r=\pm 0.487$ , no significant linear correlation

c. Critical values: $r=\pm 0.396$ , significant linear correlation

d. Critical values: $r=\pm 0.487$ , significant linear correlation

a. Critical values: $r=\pm 0.396$, no significant linear correlation

b. Critical values: $r=\pm 0.487$ , no significant linear correlation

c. Critical values: $r=\pm 0.396$ , significant linear correlation

d. Critical values: $r=\pm 0.487$ , significant linear correlation

asked 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?

asked 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.

asked 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

$$\overline{y}\sum _{r=1}^{n}{x}_{r}^{2}=\overline{x}\sum _{r=1}^{n}{x}_{r}{y}_{r}$$

where $(\overline{x},\overline{y})$ is the mean point of the sample.

$$\overline{y}\sum _{r=1}^{n}{x}_{r}^{2}=\overline{x}\sum _{r=1}^{n}{x}_{r}{y}_{r}$$

where $(\overline{x},\overline{y})$ is the mean point of the sample.