 # Lession - #1516 Regression Slope Test

hypothesis test to determine whether there's a significant linear relationship between an independent variable X and a dependent variableY.

The test focuses on the slope of the regression line

``````
Y = Β0 Β1X
``````

where Β0 is a constant, Β1 is the slope( also called the regression coefficient>
, X is the value of the independent variable, and Y is the value of the dependent variable.

Still, we will conclude that there's a significant relationship between the independent and dependent variables, If we find that the slope of the regression line is significantly different from zero.

#### Test Requirements

The approach described in this assignment is valid whenever the standard requirements for simple linear regression are met.

The dependent variable Y has a linear relationship to the independent variableX.

For each value of X, the probability distribution of Y has the same standard deviation σ.

For any given value of X,

The Y values are independent.

The Y values are roughly typically distributed( i.e., symmetric and unimodal>
. A little skewness is ok if the sample size is large.

The test procedure consists of four way( 1>
state the suppositions,( 2>
formulate an analysis plan,( 3>
analyze sample data, and( 4>
interpret results.

#### State the Hypotheses

still, the slope won't equal zero, If there's a significant linear relationship between the independent variable X and the dependent variableY.

``````
Ho Β1 = 0

Ha Β1 ≠ 0
``````

The null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope isn't equal to zero.

#### Formulate an Analysis Plan

The analysis plan describes how to use sample data to accept or reject the null hypothesis. The plan should specify the following elements.

Significance level. frequently, researchers choose significance levels equal to0.01,0.05, or0.10; but any value between 0 and 1 can be used.

Test method. Use a linear regression t- test to determine whether the slope of the regression line differs significantly from zero.