## Regression/Hypothesis testing - UCLA Statistics

### Simple Linear Regression Analysis - ReliaWiki

The inferences and interpretations made in multiple linear regression are similar to those (this is the null hypothesis.

Run Multiple Regression Analysis using the QI Home » Hypothesis Test » Multiple Regression.

### This chapter discusses simple linear regression analysis while a ..

This is called the **null hypothesis**. Null meaning nothing. And the hypothesis is that nothing is there in our data, no differences from what we expect except chance variation or chance error.

Plots of residuals, , similar to the ones discussed in for simple linear regression, are used to check the adequacy of a fitted multiple linear regression model. The residuals are expected to be normally distributed with a mean of zero and a constant variance of . In addition, they should not show any patterns or trends when plotted against any variable or in a time or run-order sequence. Residual plots may also be obtained using standardized and studentized residuals. Standardized residuals, , are obtained using the following equation:

## Horizontal line regression is the null hypothesis model

Simple logistic regression finds the equation that best predicts the value of the *Y* variable for each value of the *X* variable. What makes logistic regression different from linear regression is that you do not measure the *Y* variable directly; it is instead the probability of obtaining a particular value of a nominal variable. For the spider example, the values of the nominal variable are "spiders present" and "spiders absent." The *Y* variable used in logistic regression would then be the probability of spiders being present on a beach. This probability could take values from 0 to 1. The limited range of this probability would present problems if used directly in a regression, so the odds, *Y*/(1-*Y*), is used instead. (If the probability of spiders on a beach is 0.25, the odds of having spiders are 0.25/(1-0.25)=1/3. In gambling terms, this would be expressed as "3 to 1 odds *against* having spiders on a beach.") Taking the natural log of the odds makes the variable more suitable for a regression, so the result of a logistic regression is an equation that looks like this:

## Test regression slope | Real Statistics Using Excel

In Weibull++ DOE folios, information related to the test is displayed in the Regression Information table as shown in the following figure. In this table the test for is displayed in the row for the term Temperature because is the coefficient that represents the variable temperature in the regression model. The columns labeled Standard Error, T Value and P Value represent the standard error, the test statistic for the test and the value for the test, respectively. These values have been calculated for in this example. The Coefficient column represents the estimate of regression coefficients. The Effect column represents values obtained by multiplying the coefficients by a factor of 2. This value is useful in the case of two factor experiments and is explained in . Columns Low Confidence and High Confidence represent the limits of the confidence intervals for the regression coefficients and are explained in .

## Null hypothesis for linear regression - Cross Validated

The matrix is referred to as the . It contains information about the levels of the predictor variables at which the observations are obtained. The vector contains all the regression coefficients. To obtain the regression model, should be known. is estimated using least square estimates. The following equation is used:

## I am confused about the null hypothesis for linear regression

If you are mainly interested in using the *P* value for hypothesis testing, to see whether there is a relationship between the two variables, it doesn't matter whether you call the statistical test a regression or correlation. If you are interested in comparing the strength of the relationship (*r*^{2}) to the strength of other relationships, you are doing a correlation and should design your experiment so that you measure *X* and *Y* on a random sample of individuals. If you determine the *X* values before you do the experiment, you are doing a regression and shouldn't interpret the *r*^{2} as an estimate of something general about the population you've observed.